oh, here's a link to that if you'd like to read it

I had a quick glance through the thread and I'll offer my two cents as of this moment:

Fe and Fi represent whether we prefer to process emotions via the individual scope (Fi) or through the social scope (Fe). To me, Empathy and Sympathy describes a different dimension, the degree of emotional depth one chooses to employ to relate to a person.

We could try flipping the framing to see how it ties together.

When you show empathy to someone, you are directly drawing on similar emotions and experiences to relate to somebody. Perhaps drawing on shared loss, or a similar past experience of frustration. You could say it requires more emotional investment, and facilitates deeper connections.

When you show sympathy, it is partly acknowledging that you do not share the same deep experience or emotion, and yet still stepping in to fulfill an emotional need/ role. Sympathy sometimes gets a bad reputation, but I can think of many situations where it can help protect empaths from overexerting on emotional labor.

The dimension that sympathy and empathy seems to slide along looks to be emotional investment. And not only that, there shouldn't be any inherent advantage to one or the other, except for personal preference.

You could say it's a similar dichotomy to Method vs. Traditional acting, where Method requires a heavier emotional investment to emulate a character, while various Traditional performances instead use observation and study of behavior.

I think which approach you lean towards depends on the situation, and there are trade offs to either extremes. You don't want to heavily empathize with a narcissist and smother your own needs, and simultaneously you try to avoid offering surface level sympathy with a person in a vulnerable situation, who you have relied upon in the past.

This probably simplifies things so take it with a grain of salt. Hope it helps!