What are the differences between Super Mario 64 (N64) and Super Mario 64 DS?

What are the differences between Super Mario 64 for the Nintendo 64 and Super Mario 64 DS for the Nintendo DS? Are they just the same game or are there any significant differences?

The DS version's main feature is a few extra playable characters with special abilities. The Wikipedia article covers most of the functional differences.

However, I would like to bring attention to the main difference in my head: the DS controls are horrible. Since the DS doesn't have an analog stick, you are forced to use either the DPad or the stylus. Both controls are clunkier and more annoying than their 64 counterparts.

I loved the 64 version and got every star in it, and really wanted to play it again with new characters. Unfortunately, the DS controls made me unable to stand playing the DS version for more than a few levels in. It would be nice if they would rereleased the rerelease on the Wii instead so I have some chance of ever completing it. However, if you play it on a 3DS, you can use the circle pad in place of the DPad, which fixes all of those problems. On 3DS, the DS version controls just fine.

According to Wikipedia, there were a few additions / changes to the DS version:

Yoshi, Luigi, and Wario are additional playable characters, and the game features slightly altered graphics, additional stars, courses, touchscreen mini-games, and a multiplayer mode.

DS version's graphics are way better than the N64 version. There are new characters and all have special abilities (which are listed bellow) and 30 more power stars. The only way to make the controlls better is, to buy a 3ds.

Yoshi- Fire Breath, Mario- Float, Luigi- Invisibility, Wario- Metal Wario