Power-wise, I thought any difference between Gamecube and the other two consoles was negligible. There's no reason to turn away from the Gamecube by saying it had inferior graphics to the PS2 or anything like that.
Just to boil down what others have same, it's the 3rd party support and the lack of a DVD player.
Now, Gamecube did have some great games. Smash Bros Melee, Eternal Darkness, Mario Sunshine (imo), and a few others. It just didn't have AS MANY great games as the PS2, which churned out hits like a mofo.
I mean, PS2 was like... a golden machine. One of the greatest libraries of all time. But I have a lot of respect for the Gamecube. It was a better console for that generation than the Wii is for this generation.