Thanks to BoneSatyr, there's more info on composers (sadly no breakdowns):
Mighty Final Fight: Setsuo Yamamoto, Yuko Takehara
Final Fight/Final Fight Guy: Toshio Kajino
Final Fight 2: Yasuaki Fujita, Mari Yamaguchi, Yuki Iwai, Setsuo Yamamoto, Yuuko Takehara, Tatsuya Nishimura
Final Fight Tough: Katsunari Kitajima
Game has no credits, but Kitajima's
homepage has this on his works
Tracks 21-38: Final Fight One: Toshio Kajino, Seiko Kobuchi
Game reuses SNES Final Fight/Final Fight Guy credits with Kajino, but as Dag checked from liners, I think it's Kobuchi's work fully.
Final Fight Revenge: Jim Wallace
Final Fight CD: T's MUSIC
And all nonlinked stuff has been checked from various longplays on youtube (Imagine if you couldn't skip on youtube vids :D)
Also, BoneSatyr said that X68000 version sounded exactly as originals but with different sound board, so probably no arranging was done, just porting. So probably same people did same tracks.
Probably should check what tracks are used on the arranged tracks on the fifth cd to get some composer credits for those. And did Alfh Lyra/Alph Lyla arrange them (pity that none of those CAPCOM-00x albums have good booklets/credits).