Don't get me wrong, Chrono Cross is an excellent game. Better than the average crap regurgitated by game studios these days. But it fails at several crucial points.
Even if, for a moment, you ignore the existence of Chrono Trigger, Cross still has several shortcomings. Having 40+ characters was, in my opinion, a failed experiment. Everyone could join your party, everyone could use almost all techs (Yes, the element system is badly designed, IMO. More about that in another post, perhaps.) and everyone spoke the same lines, modified by accent. Exciting. And the pacing of the plot is terrible. I mean, absolutely atrocious. Opassa Beach Exposition is a complete disaster. This tarnishes an otherwise interesting story, because pacing is as important as plot. I also don't care for the overall misanthropic mood of the game, but that's my personal taste. Though let's admit the whole "evil humans hurting the nature-loving peoples" is as cliché as it gets.
But here's the thing: You can't ignore the existence of Trigger. It doesn't matter if you want to call it a sequel or whatever, Cross is a direct continuation of Trigger's story. And, for several reasons that I don't have the time to get into right now, Cross is a terrible sequel (whatever you want to call it, the specific word doesn't matter) to Trigger. If Kato wanted Cross to be judged independently of Trigger and stand on its own merits, he should have made the game without any connection to Trigger. Because, let's face it, the setting, characters, story, all that could've easily been modified or rewritten to have no connection to Trigger. But Kato opened the door when he made his game a continuation of another, and when he did that he introduced certain expectations for this continuation that were not met. Basically, he tried to have his cake and eat it too.