I played CC.

Sure, the story is connected - Kid being raised by Lucca, the Time Devourer being Lavos, Guile being strongly hinted to be Magus, all that thing. But the loads of characters make you look at the big picture, instead of focusing on their individual personalities; the theme (dimensional travel vs. time travel) is different; and the battle system is nothing alike. Those things are actually improvements, but at least for me, they make it that CC doesn't scratch the same itch as CT.

And there's always that lingering melancholy in Chrono Cross that is at the same time beautiful and completely unlike the "happy" Chrono Trigger.

That's why I say that it's a great game, but an awful sequel. It doesn't have the elements that make you say "THAT is Chrono Trigger 2!", but it's fun and in certain aspects better than CT.