Unfortunately... it was usually xbox>PS2>GC.
The GC had the superior hardware for rendering, but many 3rd party devs didn't even both because of the low install base. They just pushed the PS2 version onto GC hardware, and cut FMVs or whatever else was necessary to fit it onto the 1.5GB discs.
I remember Enter The Matrix and one Lord of the Rings game being released as 2-disc games on GameCube, while the other consoles got the whole game on one disc. But at least the Cube did get the full game both times.
Killer7 was also released on 2 discs on GameCube and one disc on PS2, yet the GC version was FAR superior. Better colors, smoother framerate, even better controls iirc. GameCube was definitely the platform of choice for this game.
Also I remember quite some PS2 ports having really unsaturated colors.
Sega Soccer Slam for example. Xbox and GC versions were pretty much identical, the PS2 versions though looks like a grey-ish mess.
I also think that Need for Speed Underground 2 looked worse on GameCube than on Xbox and PS2 due to low resolution textures? Could be wrong on that one.
Also someone said or implied that Prince of Persia Warrior Within and The Two Thrones looked worse on GameCube?
That is not true. The GameCube version of Warrior Within at least looks better to me than the PS2 version, due to colors once again, but also because the framerate got a lot worse on PS2 than it did on GameCube. Can't comment on the Xbox version though.
Also, whoever said that the GameCube version of THPS3 and/or 4 didn't have a Skate Park editor: You are wrong. There is a Skate Park editor in both games. I know I had TREMENDOUS amounts of fun using it. Still got my parks on my memory card even.