Better Story? FFVI, and it's not close.

Better Characters? FFVI, though this is close.

Better Gameplay? Chrono Trigger. This isn't close either.

Better Soundtrack? FFVI, though this is also close. However, the three best songs either game features are all in FFVI (Dancing Mad, the opera, the ending theme).

Better World/Towns? FFVI, though some of CT's individual locations (Zeal) are arguably better than anything in FFVI.

I never played either in their heyday either.