I also really enjoyed, and still do, the music score in Chrono Cross. I think that was probably my biggest motivation to keep playing it when I first got it. And, uh, I'm probably going to get some crap for this, but I like Lynx. Not for how he's a jerk, but his character design.
Everybody loves the music.
However, this is just personal opinion, I find the character designs to be (mostly) forgettable and overly-intricate somehow at the same time, mostly because of how many there are, it seemed like they were desperate to get them to look different from each other and only a few of them ended up anywhere near as iconic as Trigger's designs, again, just my opinion. The ones I like, though (and here's the part where you don't get any crap at all! )happen to be Serge, Glenn, Riddel, and Lynx for sure, among a few others.
Some of them are downright silly for no reason (NeoFio, Starky, Poshul, Mojo),
and some just seem out of place or out of time (seriously wtf is up with Nikki),
and some are just there as references or homages to CT characters who make less sense being there than the actual CT characters would:
Guile should have been Magus (or Magil, I don't care which, either way he should have had character and backstory),
Turnip should have just been Frog (and/or Glenn should have been CT's Glenn, but I'd still want CC's Glenn in the game, just maybe with a different name, like maybe...Cyrus?),
Miguel should have been Crono (and Leena's mom should have been recognizably Marle),
Leah should have been Ayla, Luccia should have been Lucca,
Kid seemed like they were trying to repeat the success of Marle^10 to me but should have been much more like Schala, all things considered
and Pierre should have been Tata(he could have come with CT's Glenn as an apprentice)