In terms of graphics I'd actually argue Chrono Trigger was a more aesthetically pleasing visual experience. I was never able to get into Chrono Cross fully, I never got a full sense of immersion that I got from other games. I didn't finish Chrono Trigger either though, but the story and characters were very well presented. I think many 3D games from the PS1 were hard to look at xD. They were charming in their own ways though :3.
I agree with Covarr on the music, I haven't played the game in years and I can still hear the songs in my head. I can't remember any from from Cross, which I played for a few hours. It felt like a well constructed game though, I just wasn't able to get into it emotionally and invest myself into it because for whatever reason I couldn't bring myself to get immersed into the world and characters..
The same problem I have with Dragon Age and Mass Effect series really, I can appreciate the game in many ways, and see it was a wonderful work of art and an experience to love for what it is, but I cannot bring myself to keep playing it out. For whatever reason that is.
Still, Cross looks like a good game. I might have to give it a go again sometime.