You're playing it wrong: Super Mario 64

From thecrankyhermit

Super Mario was originally released in 1996 on the Nintendo 64 as its flagship title, on launch. In 2004, a Nintendo DS version was released, adding Yoshi, Wario, and Luigi as playable characters, more levels, more stars, a minimap feature, enhanced graphics, and some new minigames.

Don't play this version when the original is available. First of all, the lack of an analog stick *really* hurts the game. That alone is a big enough regression to keep it from replacing the original. Movement uses the d-pad with Y for sprinting. You can also move with the stylus, but it's clumsy and awkward, and mainly useful when walking very slowly, or spinning around in circles.

The new characters do more harm than good. Luigi is cool, but Yoshi and Wario are sluggish and no fun to play as. You can play through most of the game as Mario, but you start off with Yoshi and must play through a good chunk of the game as him before you unlock Mario. Many of the stars can also only be collected as a specific character. The characters also alter the game's pacing - in the original, there were secret levels with switches that, when pressed, would create new powerups throughout the entire game. Finding such a level was an epic moment - completing it proper would mean changing the face of the entire game, permanently. The levels still exist, but only one of them still has a switch - the rest only have stars to find. Instead of switches for different powerups, the character you play as determines what powerup you get.

Also, the graphics are allegedly enhanced, but I don't really see it. Mario and Bowser have better models, but the texture quality is mixed, and the N64 has better resolution. With emulation, you can have even more resolution.

So, stick to the N64 version. You can emulate it legally on Virtual Console.

Graphics comparison:

Nintendo 64 (emulated)
Nintendo DS (top)
Nintendo DS (bottom)