Bust a Groove is a hybrid music/fighting game combined PaRappa the Rapper-like rhythm-based gameplay with fighting game elements, including special moves designed to damage the opponent and a focus on head-to-head competitive play.
It's not the best or deepest rhythm game on the PS1 (actually it might be), but it almost certainly has the dopest music. Pretty sure the seeds of my love for disco were planted here way back when.