Really if we think about this ... with the GBC/N64 or GBA/GCN ... you really needed a Nintendo console. You couldn't really run any type of 3D game on a GBC or GBA. Mario 64 or Zelda: OoT or Smash Bros. Melee just weren't possibly on handhelds.
When DS came out, it had rudimentary 3D ability comparable to the Playstation 1/N64. It could do some Nintendo games OK in 3D, but nothing special.
The 3DS can run Nintendo IP with fairly reasonable 3D visuals. It has the first new 3D Mario, it will have the first handheld Smash Brothers, etc.
But next Nintendo handheld ... even if its just on par with a Vita + more RAM ... should be able to run most Nintendo IP at a pretty darn expressive level of visuals. We're talking something that should be able to run a very nice version of even Nintendo's more taxing visual franchises like Metroid Prime or Zelda. It would be significantly more advanced than the Twilight Princess or Prime 3 Corruption engines. Or even Mario Galaxy 1/2.
Which kinda leads me to think ... that more than anything may be the death knell for the Nintendo console (if various other factors aren't).
If you're a consumer and you can get a very pretty looking Mario or Zelda game on your handheld, I think you're going to be less apt to buy a seperate $200-$300 console for something that's slightly better looking. Nintendo is not really one to push ridiculously budgeted games anyway, even if you gave them a PS4 level chip, Mario Kart would probably look mostly the same, just running in a higher resolution with more AA or someting.