Tricky.
I have absolutely no desire to join in either lifestyle, though probably find furries harder to get along with on the day to day.
On the other hand furries tend to be happy go lucky where there is only so much faux depression I can deal with (and so much is about 5 minutes). Furries have also provided some interesting programs and tools over the years whereas seen as nobody has yet made the ability to make code in bad poetry (bad poetry magic having long since been disproven) then no emo has ever programmed or built something that I am aware of, much less find useful.
If it is last call in a club then might have to contemplate emo as I can at least squint and imagine an actually attractive goth or techno cyber dancing type. Though one wonders if it is even worth the effort and the enjoyability of such an act might be up for debate; faux depression, actual depression, still unsatisfying starfish... and while I might ride a wolf or dragon to war it is not for fun times, especially not if various "have you seen this?" images and videos glimpsed over the course of my computer fixing adventures are indeed representative of the appendages to be utilised for fun.
To that end I might say "fuck that" but I think we literally came to the opposite conclusion in the lines above.
I don't know if there is such a thing as furry music but if we can agree on something like
then I am OK with that.
Emo music... likely to involve me finding the nearest high bridge after about the third hour, not for me but to throw them and their music off with it.