I relate to both Fe and Te very strongly. Ultimately though, what I use is Fe. It's more that I understand how and why Te works well in others, even if I don't get the minutia of it. So long as the other Te person isn't against or out of alignment with me, we work well together.
Both of them are directed towards plans, function, group dynamics, right/wrong, getting to the goal, and being productive. The best way I delineate them is Fe works with subjectivity, where as Te works with objectivity.
Neither is better than the other, and they aim for the same things, but what the work with while similar, is quite different. I definitely work with subjectivity and I have no problem with it. Granted, there are some areas I demand objectivity as that's how you must be to make something right, but I'm speaking in more of a general sense. This is most apparent when dealing with other people. With me, Fe leads me to see the "flow" of groups of people, how they relate, move, and work. I consider this information to be vitally important and it happens automatically. Te doesn't do that. While it recognizes group dynamics just as well, it does so in a more objective pragmatic manner. There has to be an explicit purpose and use that can be defined and worked with clearly. You won't often find them saying something like "the quality of this persons presence leads others to feel x". It's simply unimportant.
Fe is also more indirect with things. It doesn't have to be linear, and is ok with the messiness of the social world and interactions. There is an unspoken pattern to it. To Te, this is just confusing and a distraction. To Te being direct and straight forwards cuts through the bullshit and gets to the heart of the matter much more quickly and cleanly.
I ultimately define it as this:
Fe: Subjectively analyze objective information
Te: Objectively analyze objective information
