It's rare that I think game remixes should replace the original track (let's face it, most video game remixes are, well, poor).
But were Chrono Trigger ever remade (again), I would have to say that this sort of a piece would be an excellent piece to, at the very least, use as inspiration for Schala's theme.
She was a character who was destined to death, and while the game's creators gave her a more down-trodden theme, it just didn't capture the full essence of her sacrifice. This piece, I feel, speaks with a more powerful voice, just about who and what she was.
I wasn't sure about the sax at first, but the more I listen to it, the more I feel that it has the perfect sound to compliment the piano for this piece.
Anyway, I've not heard your previous make of this piece, so I can't quite say much about a comparison between the two, but I've only minor complaints about this version, which have already been addressed by others here.