As I understand it, Fi is mostly about forming one's own opinion (and perhaps projecting it or pushing it on others), whereas Ne is more about actually noticing other people.
For example, Personalitypage.com says that if a given INFP is too Fi-focused, he'll be self-centered and oblivious to the people around him. To get more balance in life, he needs to consciously develop his Ne by paying more notice to the people around him. See the section entitled "Potential Problem Areas" at
http://www.personalitypage.com/html/INFP_per.html
Personally as an INFP, when I walk in a room I don't even really notice the mood of the people there. I'm one of those self-centered Fi-focused people with kind of weak Ne: When I walk into a room I'm mainly thinking in terms of what I want to achieve in that room. If it even occurs to me to notice the mood of the other people in the room, then I really have to tune in my Ne and pay attention, like tuning in a radio station on the radio.
IMO, the only place where Fi gives me any real psychological insight into others is when they describe a problem and ask for advice. Having spent a lifetime rummaging around in my own head, I like to think that I'm a bit of an amateur psychologist and can project my own experience out onto others. So I'm quick to offer advice based on quick exploration of a personal problem or situation. And actually I'm not all that bad at it.
But in fairness to the other person, I do try to keep in mind that what I'm doing is essentially projection of my own situation onto another person, i.e., I'm very good at putting myself in other people's shoes. However, frequently new information emerges in the exchange of information which forces me to change my diagnosis and my advice. That again indicates to me again that my Fi is largely projection and prediction rather than any particular ability to actually "read" the other person. (Again, that latter skill would belong to Ne, which I'm actually kind of weak at.)
Just my opinion, of course. I don't pretend to be an expert on this stuff.