The control, the sense of inertia and actually being in a 3d space. If you take a Crash or Naughty Dog platformer, you could apply the level design in those games directly to a 2d game, just from an overhead perspective.
The platforming and layout of Mario 64 could not be translated into 2d topdown, because it used the actual 3d space. This extends into SMS even if you think of the Jackie Chan sorta jumping/wall climbing you do in that game.
Mechanically, most modern 3d platformers are like a cheap radio control car, that has four basic directions it can go. Up, down, left, right. Mario on the other hand is like a highly manueverable RC helicopter that can twist around, rise and fall, diagonal, curve and strafe.