Sympathy is when you have compassion but don't necessarily share the feeling. With empathy, on the other hand, you share the feeling.
If a woman talks about the problems of childbirth, as a man I sympathize with her plight. I understand that she was in distress and pain, and I feel bad for her. But I haven't experienced it myself, so I can't really empathize to the point of feeling what she felt.
OTOH, when someone talks of losing a job, I empathize. I've been there, and I can remember exactly how that felt. In a discussion about the subject, I can relate my own experiences and help analyze the nature of the experience with the other person.
Link:
Empathy vs. sympathy - Grammarist
Anyway, that has little or nothing to do with Fe vs. Fi. Anyone can do both sympathy and empathy, depending on their depth of feeling and shared experience for what someone else is going through.
Fe vs Fi is more about the following:
Fe reacts to emotional events or data in a direct, in-the-moment, from-the-gut manner. Since it's an extroverted function, it functions out in the world and is more immediate.
By comparison, Fi is an introverted fucntion and is more about analyzing emotional data. It brings the data down into a private laboratory, dissects them, creates systems (philosophies, ethics and value systems) on how to handle them, and then uses an extroverted function (Ne, Se, etc.) to apply those systems in the world. Since Fi pulls emotional data down into a private space, the result tends to be more "me-oriented": How do *I* relate to these things.
Anyway, none of that has anything to do with sympathy or empathy. One might say that Fe is more empathetic since it's more from-the-gut. Or one might argue that Fi is more empathetic, because it's more about how *I* relate to things. But really, it's a "red herring" debate. There's no real correlation. Fi and Fe are more about *how* people process emotional data, and not necessarily about the resulting feelings or responses (which can differ greatly, or be very similar).
*****************
[ETA:]
The contrast between Fe and Fi applies to the other functions as well.
Se riffs directly with stuff happening out in the world; Si analyzes data in an internal laboratory to extract patterns and rules.
Ne brainstorms lots of ad-hoc solutions directly in the world; Ni analyzes data in an internal laboratory to extract a single optimal solution or principle for dealing with a situation.
Te organizes and finds fixes directly in the world; Ti analyzes data in an internal laboratory to create logical and legalistic systems for organizing the world.
I think this makes some good points.....especially about the basic I/E difference....although I would say that Fe is not just more immediate real world response, but a rational mentality that is geared towards action to bring various elements into a harmony (which doesn't mean "peace", but all functioning to support some value they have; these values are usually a matter of Pi ideas of how reality is or could be, or else the person may be overly swayed by their environment [true of all extroverts]).
I would also add that the presence of iNtuition* in a mentality brings this addition of what I call "grasping foreign feelings" or experiences. To me, this means Fi or INFPs are not all about their own experience at all.
*
(Sensing seems to rely more on concrete data clues, ie body language, or firsthand experience or direct relating from people whose experience they trust).
Growing up, I did not relate easily to other people. I felt a gulf between my inner experience and theirs. I think the development of iNtuition to complement Feeling led to my being able to grasp the "essence" of a person and to simulate that in my brain and then understand how they feel in their circumstance, not how I would feel. Because even in the same situation, we are different people with different histories and makeup.
For me, empathy is
understanding, not necesarily absorbing an emotion (which I heavily resist). The shared feeling is the recognition of how it connects to the basic human experience. While a particular experience may not incur, say, sadness in myself, I do know what sadness feels like. I cannot determine what someone else's response indicates unless I know their context. Value is context dependent. If I can get a grasp of their basic nature and life experience, then I know what context their emotion exists in and have a better idea of what it really MEANS. What is it actually signaling?
Some of this is still Fi too....Dario Nardi thinks INFPs use intent, whole-brained listening to "get to the core of someone's psychology", that basically, we are the best listeners, because we put aside our own thoughts to just absorb.
The exploration of your own inner world and, as you say, creating these value systems, is basically mapping out a prototype for the human experience. Fe types tend to simply focus more on understanding how interpersonal dynamics work, by observing and participating in them, and they seem to focus on building a system in real time that works towards some idealized end for human relationships. Obviously, lots of crossover between the two.
However, I think the focus for Fi on the creation/refinement of its value systems, and while Pe may explore how they could manifest in the real world, Pe is also using its exploration to refine these systems. This is particularly true with
adult xxFPs.
Interestingly, in Nardi's observations, the IXFPs did not show themselves swayed at ALL after engaging in this listening! Actually, most quickly asserted their own feelings and thoughts, often unchanged by what they just intently listened to.
Some may call this stubborness when those people are trying to convince the IxFP of something else, but considering you thoroughly listened to what they said, it just means that their reason (or lack thereof) failed to trump yours. In other words, the Fi type created this little simulation of you, determined why you feel as you do, considered if your reasoning (or lack thereof) actually upholds whatever value is at stake, and then they compared that to their previously, deeply, thoroughly crafted system for How People Work. Your reasoning and value judgment are deemed flawed. But we really, really listened. Other times, if empathizing, we just use that info to refine our understanding. It is another data point in the system. Sometimes we dont know what to do with it or dont take on any responsbility, so it can make an IxFP look "cold".
Considering this, the ideas in the OP are too black and white to grasp that "empathy" can be and often is tempered by rational thinking. The push for increased empathy is to temper rational thinking. The two are complementary and to deny the relevance and useful power of one is silly. I think there has been stronger denial of empathy or a dismissal of it as weak sentimentalism because of its association with femininity. It is a receptive, internal process, not one of action.
The end of the OP rushes over that idea, but even that little paragraph unravels everything before it by suggesting what most people know is true, and what [MENTION=22236]YUI[/MENTION] summed up - emotions are data points, empathy is an experience to consider as data, and reason is used to form conclusions.
Jung knew this about Feeling types too....they are not called "emotional types" or "empathetic types", but rational types whose focus makes emotion relevant data. They are trying to determine the value things have in the human experience, and emotions are useful signals.
The reason people make jokes about extreme T types being robots is because a robot has no motivation. It performs a sequence to produce a particular end result. How do we determine what end result is useful or good, WHY it is useful or good, etc? Feeling tells us what it means and what value it has for our human experience.
Empathy may be an initial motivating factor, but it cannot determine value alone and suggest an ideal end result for action; it is just information. Feeling reasoning must be used. I definitely have seen what I call "misapplied empathy" or "excessive emapthy" in which people seem to be blown here and there depending on what is pulling their heart strings. This is NOT Feeling as a rational process at all. Again, iNtuition can clue us into the unknown, by suggesting the possible or probable end results of certain actions. Will a particular action actually lead to the ideal end result (or move closer to that goal)? I think Thinking is necessary to tell us how we can strategize to get there.
Without empathy though, we become pretty solipsistic and myopic.