Yes, maybe even slightly more powerful than the Vita!

Some stuff on the gamecube is better, others are better on the 3DS (Shaders, etc.). In terms of CPU, definitely GC though.

Plus the 3DS small screen helps.

Next handheld should be good though

That's poppycock.

3DS has a far more modern graphics feature set and 2-4 times as much RAM.

It's pretty close but I'd say Gamecube.

Agree. Just look at the colors, almost all GC (and PS2/XB) games looks more monotonous and "gray" to me compared to modern games. Even the colourful ones. When I see old 6th generation screenshots I feel artists has developed a lot. 

Also, not just the colours, the overall design in modern games like 3DS, placement and stuff like that. Everything is just more thoroughly planned, and that makes new games look better. But if it's more powerful than GC? I don't know. 

Edit: New shader is what I was talking about. 

Not to be nitpicky. I think 3ds probably has better graphics but it's not a gaming console. It's a gaming mobile device..just saying

Before anyone argues..http://www.merriam-webster.com/dictionary/console :  an electronic system that connects to a display (as a television set) and is used primarily to play video games

So no its not a console..again just saying. It would be like calling a console, or a moble device a PC, which is just silly and would get ya tons of weird looks. Even tho they are all basically computers their hardware makeup splits them up into well defined sub categories of Computer. Just like how all gaming machines/platforms are seperated into well defined sub=categories that should be respected and acknowledged. Otherwise it would be like looking at a carrot and calling it a potato and expecting anyone to understand, let alone take ya seriously.

Gamecube is more powerful. It can handle better textures, higher poly characters and environments. But 3DS can do more with shaders and lighting effects, hence why Resident evil Revelations kind of looks like it could be on the 360.

F-Zero GX, Wind Waker, Rogue Squadron, and RE4 look better than any 3DS game barring RE Revealtions which largely relies on shaders and narrow corridors (allowing the game to push all its polys into a shorter area).

GameCube has better poly pushing prowess and texturing, 3DS wins on lighting/shaders.