My take is that Kato is interested in darkness. His games are typically quite dark, and 12,000 BC - for which Kato is solely responsible - is the darkest part of CT. It is also the most enduring and brilliant part of Chrono Trigger. But it is largely so, I believe, because it is the darkest and most dramatic part of a story which is otherwise very hopeful and optimistic. The contributions of the other members of the team complemented 12,000 BC and allowed it to be as impacting as it was.
In short, in CC, Kato was director of his own project and had to share less of the spotlight with others; and so he had to edit himself less, which can be fatal for a storyteller, no matter how capable they are. It was, imho, such a bad thing because although 12,000 BC is so meaningful and amazing and is, in fact, my favorite part of any video game ever, IT IS NOT ALL THERE IS TO CT.
(Also, judging by CC, Kato either lost everything he knew about how to plot a video game scenario effectively or didn't have one of the CT guys helping him. It is ironic to me that Chrono Trigger has such a beautiful, simple, elegant, symmetrical plot while the plot of its sequel is an unholy mess. But that's neither here nor there...)
Personally, I will always admire Kato for his contribution to CT and for some truly brilliant moments in CC, but I don't buy that whole growing up and taking things seriously means darkness meme. To me, so much of what's stayed with me about CT was how sweet and poignant it is, how much hope it offers. As I grow older, it means even more than it used to.
(I don't mean to be terribly down on CC. I love Kato, I love Schala, and moments of CC are just incredible, like the ending. But I do believe he dropped the ball in a big way with this sequel.)