Specs:

3DS:
266 MHz ARM 11 Processor Dual Core
Approx 133 MHz Pica 200 Graphics Processor
128 MB of RAM
4-6 MB of Video RAM

Gamecube:
465 MHz Single core 'Flipper' CPU
162 MHz GPU
40 MB of RAM
4 MB video RAM

Gamecube runs higher-res textures and can push more polygons than 3DS, even without counting the 3D mode which should cripple performance a lot on a 3DS. 3DS has the edge in the shader department and anti-aliasing usage seems to be less expensive than it was on GC(every Capcom game uses FSAA in 2D mode).

GameCube with more power, 3DS with newer shade tech. GameCube also output a slightly higher resolution even if you account for both screenson the 3DS.

Gamecube is technically more powerful and really we never saw it maxed out much in its life unfortunately, but the 3DS isn't far behind.

Those aren't 3DS images actually, they're all a higher resolution than the 3DS can do. Any actual 3DS screenshots would be 400x240.

Quote Tree Shortened - Conegamer

As many have said already, each has their own strengths, much like, say, the Wii vs the original Xbox.

GCN pushes more polygons and a higher screen resolution.

3DS has more advanced shaders.

GameCube. MKDD looks better than that. That's the MKDD beta. and the Resident evil comparison is unfair. The best looking RE for GameCube is Resident evil remake. The best looking RE for 3DS is revelations

Gamecube, 3DS isn't that far off though.

Well, technical stuff aside (GameCube > 3DS, but 3DS can do more modern techniques), I'd say it's a mixed bag. GameCube wins at some points while 3DS wins at others. It's quite balanced actually.

Both Luigi's Mansions and the Mario's look quite comparable. On one hand we haven't seen things like Rogue Squadron and Twilight Princess on 3DS, but on the other RE: Revelations exists.

Around the same.