Well, I admit the storyline isn't its best quality, and that its prequel may have been more coherent... but, oh yes, its artistic potency, in general, is unmatched I think. Music being incredibly beautiful, as you mention... I listen to it constantly on my phone while out and about.
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I got lost in all its artistic perfection to care about any failings in plot, to be honest.
But, even still, parallel dimensions is a cool concept to deal with... and I don't think it features in many other games (Chrono Trigger, on the other hand, was more about plain time travel - still amazing how some things done in one era can completely change another (I still remember the awesomeness of planting a seed in some future desert only to go there centuries later to find a whole forest!))
Chrono Cross asks "what if...?"
Don't get me wrong, visual and musical appeal are valid aspirations for a game. It really helps draw me into the fantasy world when there's so much to look at and listen to that's unique to what I'm playing, but it tends to end with the game. I remember replaying Chrono Cross half a dozen times trying to get specific characters because I hated using guides, which was one of my favorite features at the time.