I think it's hilarious that people are trying to compare them directly against each other as if they're market rivals.
You can't compare them based on graphical or computing power.
You can't compare them based on functions or abilities.
You can't compare them based on anything that wasn't available last generation.
The comparison would be based on first party titles, third party support, how well they did in their respective generations, their lasting influence, and their success for their manufacturers.
Based on those four characteristics, I would rate Gamecube, PS3, PS3, Gamecube, Gamecube, respectively.
(1) It's hard to argue against SSBM, Wind Waker, Twilight Princess, Metroid Prime 1 & 2, and Pikmin 1 & 2, amongst others. Sony's titles don't reach across such a wide spectrum and aren't as highly regarded nowadays.
(2) Gamecube received very little third-party support, and what they did was mostly multiplatform support.
(3) PS3 has sold nearly triple what the Gamecube did, hardware-wise.
(4) Gamecube's influence was that it made Nintendo decide they had to do something drastic. If it weren't for Gamecube doing so poorly, Nintendo wouldn't have gone into motion controls, and without that, we wouldn't have Kinect or Move either.
(5) Nintendo stayed profitable through the entire lifespan of the Gamecube. Sony, on the other hand, went very red for a very long time with PS3.
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