For someone that's never played Chrono Cross (somehow), what makes it better than Trigger?
Because Trigger is probably my favorite JRPG. It's one of two that I have played all the way through multiple times.
The other being FF IX. VII will join those ranks eventually, thanks to Uplay (for selling it for $3) and HD mods.
I fell in love with the characters in Chrono Cross far easier than I did in Trigger. As much as I love Crono and Lucca and the gang, it's an older game and I think it's natural that advances in graphics and whatnot lend more connection and personality to characters. People do complain that Chrono Cross is all quantity and not quality when it comes to the characters (there's 45 or so playable ones...), but there's a massive array of side quests and character involvement of most if not all of the characters you can use, as well as obvious focus on the main ones (Serge, Kid, Lynx, etc).
Besides that, I preferred the battle style, the magic system, and general depth to the game. There's so much to do, so many secrets to uncover, characters to recruit and experiment with, etc etc. The soundtrack is the most beautiful one I've heard in a game, ever. The hand drawn environments are utterly gorgeous, the world is vibrant, not too big, not too small, varied locations and hidden areas. The story is intricate and connects with Trigger as you get farther into it, and is both interesting enough to enjoy on your first play through as well as your fourth as deep connections and understandings become clearer to you (unless you just beat the game and then read the mountains of explanations online).
I'm really overhyping the game here, but it's hard for me not to. I love Chrono Trigger as well, so realize this isn't coming from someone who hates one game in the series and loves the other. I just like Chrono Cross so much more. I haven't come across a good an RPG... ever. The closest I would put against it is Final Fantasy Tactics, which is equally deep in both gameplay and story, but even then that dark, political/religious story is much different than what's going on in Chrono Cross, and less enjoyable in my opinion.