Yeah, it's probably best to play Chrono Trigger first, because it is such a great game, and it will stem a better appreciation for Cross. But I think you could play Chrono Cross first too and not miss out on much
Chrono Cross was never developed as a "direct" sequel to Chrono Trigger, so the games are pretty separated.
From Masato Kato (Wrote both of the games)
"Accordingly, Chrono Cross is not Chrono Trigger 2. It doesn't simply follow on from Trigger, but is another, different Chrono that interlaces with Trigger."