As somebody that I don't think I use a lot of either Fi nor Fe function, I can only try to find the differences, based on my theoretical knowledge. I hope this will still be useful, even though I will not be able to draw a lot from the personal experience.
That I don't know a lot can also be seen in my typings. This is the one that a lot of times trips me, and I can not really differentiate between them.
The difference between this two function is that one is oriented inside and the other is oriented outside. So Fe, which is oriented outside, is the one that is in charge in interacting with the outside world. So it is much more likely to have a culturally accepted emotions, much more likely to express the emotions on the outside, especially when they are appropriate emotions and it is expected to show them. This is the function that makes us sad at the funerals and laugh at jokes and lie what we think about each others appearances. I don't really understand the utility of the last one, but as far as I could tell, it is part of the social contract. I really wish I could have read it somewhere.
Fi is much more inside oriented. So these people are much more attuned to their individual feelings, and because of that, they are more likely to not freely show it to everybody that comes around. A lot of time I can see Fi being connected with the strongly felt belief, that something needs to be done for the people or for the world. I am sometimes suspicious that the notion to save the world came from these people, even though it is normally connected with the NF temperament. There are also a lot of shoulds involved. Like people should protect the planet, people should stop eating meat, or people should follow their passions.
Because of this difference, Fe is much more oriented with the general harmony among people. Because of that, since strong feelings are usually not good for total harmony, their feelings are a bit more shallow than the feelings of the Fi types. Fi types on the other hand, feel strongly about their values, and are much more likely to appreciate the individuality of each person by themselves.
But this is where my knowledge about the differences stops.