I really loved the DS version. I never got all 120 stars on the N64 original, but when the game hit the DS I not only got all 120 stars, I got all 150. The game adds 30 all-new stars, several all-new worlds, three new playable characters (Yoshi, Luigi and Wario, each with their own powers), a real-time map that doubles as analog character and camera control when you use the thumbstrap, and a host of sweet minigames (the bob-omb slingshot game is probably still the best use of the touchscreen to date).
The DS version has the best graphics, too. This is fact. For proof of this, simply compare the N64's Bowser to the DS Bowser. The DS one looks GameCube quality, like they lifted the boss battle from Luigi's Mansion and stuck it on a portable. He has nice textures on his shell, a higher polygon count and better skinjob, and superior fire effects (no more smudgy one-color flames!). Another good example is Thwomp; on the DS he has the spiny ridges he has in Galaxy, as opposed to the blue blocks of the N64 original.
The new gameplay dynamics offered by the characters (Yoshi egg-throwing ftw) and power-ups (balloon Mario!) are fun as well. All in all the DS version is the better game, but despite all my glowing praise I'd probably recommend trying the $10 Virtual Console version first. Play it with a Wavebird and experience it the way it originally came out, with controls that are far more accessible (the thumbstrap has a steep learning curve).
That's my two cents.