On the most basic level they're about the same thing: The deeply disorienting idea of a world exactly like your own, but where fundamental things have changed. Chrono Trigger explores how one's actions affect the flow of time, letting you see the world in far-flung pasts and in dystopian futures that can be altered by your adventures, while Chrono Cross explores a subtler idea: Parallel dimensions, and how different your present world is when just a few things change.
Chrono Trigger is also more popular because it has a stronger story. Chrono Cross is vast and often as directionless as the ocean that creates its key aesthetic theme. The sea is everywhere in that game, embracing incredibly detailed and lived-in towns of vibrant wood thatch and textiles that are built in confident marriage to its shores. It glitters marine and sighs quietly, and the game understands the quiet power in the ocean: some of my favorite sonic moments in Chrono Cross are the ones where the music falls silent entirely, letting the player be alone with the timeless sound of tides.
But through its key narrative device Chrono Cross creates a second world much like its first, except for a key difference: It's a world which the main character, Serge, doesn't exist, where his home village is much the same except his house is someone else's and none of his friends know him. Later, it creates a condition where Serge becomes someone else entirely.
This song, "Lost Pieces," plays when the player, by ocean boat, picks over the ruins of a particularly significant zone of the sea. To me, this sad and beautiful tone has captured the melancholy of being far adrift, of no longer belonging to a world that is otherwise completely familiar to you. As it employs a silent protagonist, Chrono Cross never tilts its hand to any of the emotions Serge might feel in response to such a tragic loss of self. But it's songs like this one, in the spaces where the game lets you alone to take it in, that create that emotion in the player.
It's why the Chrono Cross soundtrack is my favorite in gaming. Aside from its vivid and beautiful instrumentation, it's keyed to the precise feelings that the game's world wants to create, making it just fine — apt, even — for the characters to remain silent.