Don't let Chrono Trigger's excellence stray you from this great title!
Above all, Cross delivers, and greatly succeeds over it's predecessor, with the music. Chrono Trigger's music was so very memorable and so great that it's hard to imagine that it could be succeeded at all, but Chrono Cross delivers an impossibly great soundtrack.
Gameplay wise, Cross falls behind Trigger. Trigger had a great emphasis on dual and triple techs that made it very speedy but unique. Cross de-emphasizes the dual and triple techs and instead tries to add a multi-hit combat system that just isn't as fun to play with.
The story with Cross is great, but requires an unfortunately long investment to get into. The vast majority of the game is spent wondering "what does this have to do with Chrono Trigger? Does this have ANYTHING to do with Chrono Trigger?" Eventually, the game does deliver with several brain benders that satisfy, but don't quench your thirsts. The fates of the main characters from Trigger are largely left unexplained.
All in all, this is an excellent game, while not quite as good as it's predecessor and not quite what you would expect from a sequel. Actually, it's more of what you'd think of as a 'spin-off'. However, the game has merits and is a fun to play, classic JRPG with unmatched musical excellence and a compelling story. This is one of my top 10 MUST PLAY JRPG's, so it's definitely worth consideration.