I have a very good friend who is Fi dom and another very good friend who is Fe dom. I'll just kind of summarize some general patterns that I've noticed with their abilities to conquer problems.
If the Fi dom is facing some kind of trouble, she expects the rest of the people around her to respect her feelings, and she thinks it's the end of the world if that doesn't happen. She thinks that if she *feels* something, then it's right, even if she cannot back it up with logic or patterns seen from other people's feelings. Since her feeling a certain view/value automatically makes it important, she is upset when people don't respect that view/value that she holds. The things she views as important are kind of arbitrary and inconsistent imho, and when I ask her why she feels a certain way, she says things like "I can't help it. It's just how I feel."
The Fe dom, on the other hand, doesn't really have this notion of *feeling* values. He is more in tune with the people around him and how he can bring harmony to certain social dynamics. I honestly don't think he has any rigid internal value system other than he believes he needs to do what's necessary to make others around him happy. However, he does get upset if his efforts to bring social harmony go unnoticed, and he also gets upset if he is helping out somebody, and they do nothing in return but give him grief for helping them. He is the mediator that defuses the Ti/Fi based arguments that occur between my Fi dom friend and me, as he claims to understand both of our perspectives, and he doesn't put more weight on either one.