This thread seems all over the place. At first it was about Ni vs. Si, but subsequent posts raise all kinds of other issues.
Anyway, I'm no more of an expert than anyone else. But I'll try building a simplistic analogy that matches the way I understand these things. (I apologize for the length of these things; I'm starting to post like Bluewing.)
Perceiving vs. Judging
The perceiving functions are N and S. They are the cops and detectives at a police station. They investigate a problem (a crime, a dispute, whatever) and build a case for trial. Once they've either built a sufficiently strong case or simply run out of leads to follow, they deliver the case to the lawyers and the courtroom.
The judging functions are T and F. They are the lawyers (and judge) in the courtroom. They take the case from the perceiving functions, assign priorities and value to the collected evidence, compare the evidence to precedent and law, deliver a ruling, and assign bailiffs to go out and execute the ruling.
[Edit:] Please note that the progression from police station to courtroom is a "hypothetical" or "ideal" progression. As we'll see below, the progression usually isn't quite that neat and orderly when practiced in real life.
Perceiving: S vs. N
Returning to the cops and detective in the police station:
S = the cops that follow hard leads according to established procedure. The evidence that they track down will include both facts and feelings (both T and F). When working properly, the cops really don't notice whether the evidence is T or F. It's all just raw evidence to them. (It's up to the courts to prioritize T and F or throw out one or the other.)
N = the detectives that follow flimsy leads to distant locations for a big break on the case. Again, they collect both facts and feelings (both T and F). They tend to bring in a lot of circumstantial evidence, but they figure if the circumstantial evidence weaves together nicely then they probably have a pretty strong case.
The cops and detectives are based in the police station (perceiving function). Most police stations will tend to have an imbalance in the numbers: If the cops are in the majority, then the police station is considered an S function. If the detectives are in the majority, then the police station is an N function.
Introverted perceiving vs extraverted perceiving
The police station is located at a big municipal administrative building in the center of the city. The police station can either be located deep in the interior of the administrative building, far from the hubbub of the outer world (Si/Ni), or it can be located right at the main front door of the administrative building (Se/Ne).
Si/Ni: If the police station is located deep in the interior of the administrative building, then cases tend to be built carefully and at length in a quiet environment, far away from the noise and bustle of the outside world.
Se/Ne: If the police station is located right at the main front door of the administrative building, then the atmosphere is going to be much more loud and hectic. People will be coming and going with evidence, cops will bringing in bad guys, there will be sirens and gunfire, police will be rushing out on calls, etc. The station will still be sorting evidence and building cases, but under the pressure and immediacy of the moment the police may tend to act on the case themselves without bringing it to the courtroom.
Judging: T vs. F
Concerning the lawyers in the courtroom:
In the courtroom there are T lawyers and F lawyers. If the T lawyers are vastly in the majority, the first thing they'll probably do is have the F evidence thrown out of court. (The real world example would be a Thinker who is aware of the social and emotional ramifications of an issue--it's part of the evidence collected by the cops--but he deliberately chooses to discount them or disregard them entirely.) Conversely, T evidence will get thrown out if the F lawyers are numerous and strong (i.e., a Feeler who is aware of scientific evidence against his beliefs but chooses to ignore the scientific evidence).
In a courtroom that is more evenly balanced between T and F, both kinds of evidence will be retained and taken into consideration, but it will be prioritized. Priorities may change depending on the environment: In a real-world workplace environment, the T evidence will have a higher priority; at home dealing with the wife, the F evidence will have the higher priority.
Next, the evidence and case will be compared against legal and moral codes. T legal codes will prescribe analytical and logical guidelines for weighing the evidence. F moral codes will prescribe etiquette and emotional guidelines. Inevitably there will be some conflicts within and between the codes and their application to the case in hand, so there will be more prioritizing and balancing of competing directives.
But it all occurs rather quickly. Procedures, codes and priorities are pretty well established by long habit and use and precedent, and pretty quickly a decision is reached, the judge slams down the gavel, and the case is closed. The bailiff goes into action and executes the ruling.
Introverted judging vs extraverted judging
The courtroom is located in the same big municipal administrative building as the police station. If the police station is located deep in the interior of the administrative building (Ni/Si), then the courtroom is located right at the main front door of the administrative building and has to deal with all the noise and hubbub (Te/Fe). OTOH, if the police station is at the front of the building(Ne/Se), then the courtroom is tucked away deep in the interior (Ti/Fi).
Ti/Fi: If the courtroom is located deep in the interior, then cases are decided in a quiet environment, remote from the noise and action of the street.
Te/Fe: If the courtroom is located right at the main front door of the administrative building, then the atmosphere is going to be much more loud and hectic. People will be passing through with evidence and bad guys on the way to the police station, there will be sirens and gunfire, police will be rushing through the courtroom to go out on calls, etc. The courtroom will still be reviewing evidence and deciding cases, but under the pressure and immediacy of the moment the courtroom may tend to intercept and rule on some of the material passing through, without allowing it to get to the police station.
Dominant functions
In a perfectly balanced person, the police station (N/S) would gather evidence and build the case, and the courtroom (T/F) would prioritize the evidence and analyze it and then reach a ruling. Furthermore, the two functions would contribute to each other's development. For example, a strongly T courtroom would keep seeing lots of F evidence showing up in the evidence coming from the police station, and across time the courtroom would start paying attention to the F evidence alongside the T evidence. In turn, as the courtroom develops in sophistication, it will demand more sophistication, efficiency, and variety from the police station and how it does its work.
But in most people, there exists an imbalance and the stronger of the two becomes the Dominant. The Dominant tends to hijack the Auxiliary and turn it into a rubber-stamp facility.
Dominant Fi/Ti (ISTP, ISFP, INFP, INTP):
The courtroom (F/T) is powerful (Dominant) and is buried deep in the interior of the building away from the real world (Introverted). The police station is at the front of the building but it's undermanned and largely ignored (N/S, Extraverted, Auxiliary). When the cops (Se) or detectives (Ne) try to collect some evidence and bring a case to the courtroom, the court tends to reject the case outright (refusal to deal with real-world issues). Instead, the lawyers sit around in the courtroom and debate the legal and moral codes themselves. When they want to deal with the world at all, they tend to hijack the cops or detectives and make them hunt down evidence in the real world that will suit the T or F agenda of the court and the codes (seeking only real-world experiences and evidence that conform to existing prejudices and personal beliefs). The court itself tends to skew increasingly toward a one-sided T or F line-up of lawyers, since it only admits evidence and cases that support it's prejudices and pre-judgments.
That's an extreme example, of course. In real life, the imbalance is often moderate and/or may change from one time or situation to the next. For example, the individual may demonstrate a high degree of balance between Dominant and Auxiliary when in the workplace (because the person must incorporate real-world concerns), but then demonstrate imbalance at home where the person feels he is more at liberty to "be himself" (and thus the person may be very solitary and unsociable outside of work).
Dominant Ne/Se (ESTP, ESFP, ENFP, ENTP):
The police station (N/S) is powerful (Dominant) and is at the front of the building (Extraverted). The courtroom is buried deep in the interior of the building away from the real world and it's undermanned and largely ignored (T/F, Introverted, Auxiliary). The cops and police detectives are reacting to what's happening right out on the streets in front of their station, so they are rushing around from crime scene to crime scene, collecting likely suspects, and flying off to faraway place to follow whimsical leads. They are all quite active, to the point that they don't have much time for the courtroom. The courtroom still functions, but it is largely pro forma and just rubber-stamps whatever wiretap requests or search warrants or cases the cops bring.
Since the court is undeveloped, it tends to have a strong T or F leaning and basically just throws out one type of evidence or case and rubber-stamps the other. The cops don't tend to distinguish between T and F evidence, so it's no big deal to them if the court is exerting one-sided influence in that area.
This is a picture of a person largely reacting to circumstances with a strong F or T leaning. Cases don't tend to reach closure or they reach premature closure because the legal codes and prioritization procedures are weak or non-existent. Meantime the cops and/or detectives are getting involved in every crime scene, household dispute, and far away mystery that they run across.
Again, this is an extreme example. IRL there may be a more moderate imbalance, or a high degree of balance in one environment and less balance in another.
Dominant Ni/Si (ISTJ, ISFJ, INFJ, INTJ):
The police station (N/S) is powerful (Dominant) and is buried deep in the interior of the building away from the real world. The courtroom is at the front of the building and it's undermanned and largely ignored (T/F, Extraverted, Auxiliary). There is an enormous force of cops and/or detectives poring through data and leads in peace and quiet, far from the noise and hubbub of the outside world. Since the court is weak, there is no hurry to get a ruling or even to present the case. Since the case never goes to the courtroom, nothing gets prioritized or thrown out, so the cops and detective have the leisure of spinning enormous amounts of data and leads into grand cases. In case there are any flaws in the case, they prepare plans, backup plans, and backup plans for the backup plans. Since there are no legal codes and prioritization in the police station, the cops are free to experiment endlessly and try to map all kinds of data and leads in different combinations.
All this weaving and mapping of data and ideas takes a lot of energy and patience, though, and new information still coming in through the front door up by the courtroom can upset the work. So the cops/detectives hijack the weak, undermanned courtroom at the front of the building and get it to guard the doors by ruling arbitrarily against any new F input from the outside world if it's a T courtroom, or against any new T input if it's an F courtroom. Thus, the cops and detectives get increasingly invested in a built-up model or mapping on the inside, while outside parties are turned away by a strict, rigid judge at the front door who refuses to hear their evidence and simply rules against them because they don't fit the model inside.
[Again, standard disclaimers about extreme examples and degrees of balance/imbalance.)
Dominant Fe/Te (ESTJ, ESFJ, ENFJ, ENTJ):
The courtroom (F/T) is powerful (Dominant) and is at the front of the building. The police station is buried deep in the interior of the building away from the real world and it's undermanned and largely ignored (N/S, Introverted, Auxiliary). For the cops and detectives in the undermanned police station to build a case, they need data and leads. But the data and leads come from the outside world and have to be brought through the front door and through the strong courtroom before they can make it to the police station. If the courtroom is very strong and the police station is very weak, the courtroom will tend to seize the evidence (the N circumstantial evidence and the S data that are being dragged through the courtroom by the cops and detectives) as it is first brought into the building and rule on it right away, thereby closing the case before the cops and detectives ever get to play with it. The court's rulings tend to be snap decisions since the courtroom is dealing with the outside world on a real-time basis; the court's moral and legal codes tend to be fairly basic and the court tends to lean heavily to either T or F since the court is dealing only with single pieces of evidence and data rather than full-blown, potentially complex cases.
To spell this out further: Since F and T values and codes reside in the courtroom, the F or T rulings of the courtroom are authentically F and T. IOW, the judgments of a Dominant Fe/Te person shouldn't be considered fake with regard to the quality of their F and T. Instead, the problem is that they are snap decisions based on simplistic codes. Since cases aren't built up properly in the police station based on a full set of evidence and leads, the court doesn't develop much beyond what's needed for reaction to the immediate situation. In turn, a low level of development means the court skews heavily toward F or T. Meantime the strong but under-developed F court doesn't want to hear T data and vice versa, so it hijacks the cops and detectives from the police station and puts them to work keeping out any dissenting data and leads; which reinforces the vicious cycle of lack of development in the courtroom, heavy F or T leanings, and snap decisions directed at the outside world.
Again, the standard disclaimer:
That's an extreme example, of course. In real life, the imbalance is often moderate and/or may change from one time or situation to the next. For example, the individual may demonstrate a high degree of balance between Dominant and Auxiliary when in the workplace, by showing a high sensitivity for the need to deliberate carefully on decisions in accordance with official procedures, but then demonstrate imbalance at home where the person feels he is more at liberty to "be himself" (and thus the person may be very "administrative" or "directive" at home).
Summary
I don't see any "best fit" between functions. The perceiving and judging functions operate independently of each other. S data collected by the cops can be subject to either F or T rulings in the courtroom; N circumstantial evidence collected by the detectives can be subject to either F or T rulings in the courtroom;
What matters is the interplay between extraversion and introversion (IOW where the courtroom and police station are located in the building) and between dominant and auxiliary (IOW which of the two is stronger and is in a position to ignore or even hijack the other for its own purposes). Thus, you get 16 combinations of F/T/N/S, extraversion/introversion, and dominant/auxiliary. All work in very different but equally valid ways together.