Battle Arena Toshinden (PS1) had some of the best music of its generation, lots of those tunes live rent-free in my head 30 years later (especially recommend Duke's theme, but Gaia's is also awesome for a final boss theme).
Full playlist in this link below :
Also really loved the intro cinematic musics for Soul Edge (PS1, Soul Blade in Japan), and Soul Calibur II (PS2, the crescendo at the end of the intro is just amazing) :
The cinematics themselves are still great by modern standards, developpers have forgotten how to make good intros for fighting games.