The difference is that Nintendo made their brand name explode, so their userbase was bigger. The Gamecube had its image just about destroyed by the Playstation 2 and Xbox. Think about it. The Playstation 2 had Grand Theft Auto, the game where you could do just about anything, and it was really an open world. The Xbox had Halo, a game that changed console shooters forever. The Gamecube had, as its biggest game, Super Smash Bros. Melee. A great game, but not significant.
Really, if you had to make a list of reasons why the Gamecube did so badly, it would be long.
Purple, goofy looking, badly advertised, kiddy image, lack of exclusive mature titles, lack of RPGs, lack of titles that would appeal to the Japanese, severe lack of European appeal, odd disc format, no online connectivity, and much more. But I'm making myself a sandwich.