It was a fighting game released back in 1997 by THQ, Inc.
Hopefully somebody can rip the songs from the game. There are a few videos somewhere on Youtube.
I think it’s licensed music, no idea what the songs are though. I find it unusual for a fighting game to have licensed music in it.
Edit: VS. (PSX) Game Rip (http://rapidshare.com/files/324408127/VS.__PSX__Game_Rip.rar)