Its the same basic game, but it fixes all of the bugs that were left in the SNES version. It also has like 4 bonus dungeons, ultimate weapons & armor, and extra features. Its retranslated, too, and the new translation tells the full story. There was a lot left out and skipped over in the original, but the DS version restores all of that. Another thing that it has is a new ending that shows the ties to Chrono Cross, if you didn't know those already.
I didn't think it was going to be a big change when I first got it, but after playing through it twice (New Game+), you can really see the improvements.