feeling relates experiences and objects to the idea of the self. routes things thru the lens of the self. understands how it fits in/together.
Fe does it externally in the world, in a real and practical and actual be here now kind of way. it tries to interact, push, create, shape, manipulate, engineer, express, articulate, etc.
Fi does it internally. in a let me dwell on it for a while and use my deeply collected pools of expertise, knowledge, and past experience that i have stored and categorized the hell out of. i've spent a lot of time understanding what is right, so let me figure out how some ideas for you, etc
it depends on the type how these things angle along. Fi Ne shoots out lots of ideas (based on understandings of how this situation relates to the person's own subjective understandings, relationships with self, feelings of affirmation and denial ie judgments, etc) that others can use. Ni Fe locates a complex mish mash of contextual clues in its own giant Idea-Maker, the one Big Idea big picture blah blah, when it finds the specific place/position/perspective, finds the marker and highlights its bottom line, synthesizes the information and scans in all of the resolution (detail, data, etc), zooms in deeply to its particular latitude/longitude on the One Single Giant Idea it has (about the world and everyone in it), it finds a way to express it in an emotionally tailored, symbolized, meaningful way (the right voice for the job).
both fail miserably at times.
Fi has to work its way outward, Fe has to work its way inward. and the way that happens depends on the other functions. connecting feeling to expression/extroversion, connecting feeling to the development of a voice, a vocalization of desires, agendas, missions, interactions, communications, etc, especially one that is well-researched, intelligent, and cognitively sound, takes a while to get down pat.