Chrono Trigger has always been my favourite game, and I have played it on the SNES and Playstation. When it came out for DS I bought it and have played it multiple times. A friend of mine recently remarked that I have certainly gotten my money's worth out of the game.
The port to DS is flawless - the art, music, and gameplay are uncomplicated and almost identical to playing on a bigger console. The storyline is unchanged. The addition of two new (optional) areas on first playthrough, plus another available on New Game+, do not interfere with gameplay or story, but offer fun new challenges. An "extras" option on the startup menu lets you see the movies, hear the music, and see the art; a list of enemies fought and items collected is fun for completists who want to know they've gotten everything - and the techniques list is informative, if you want to be sure you've gotten them all before continuing to level up. The best part of the "extras" is the endings list, each one of which only appears once you've seen it! And of course all of these extras go with you into a New Game+.
This is definitely worth the price and the time you'll put into it.