The only thing GameCube has going for it in this competition is having the most Zelda games. It has Wind Waker, Twilight Princess, the Collector's Edition, Four Swords Adventures, and the Ocarina of Time Master Quest. It was the greatest Zelda collection ever.
But Wii has more 2-D Mario, more and better 3-D Mario, better versions of Metroid/Pikmin/RE4, better Smash Bros., online Mario Kart, Wii Sports/Resort/Fit, Monster Hunter 3, Red Steel 2, Tatsnuoko vs. Capcom, No More Heroes 2, Little King's Story, Muramasa, and many others. Dare I say the Wii has far superior 3rd party support than the GameCube?
The Wii even brought 2-D Mario, Punch-Out!!, Excite Bike, Blaster Master, and many others back from beyond the grave. And it stole Monster Hunter and Dragon Quest from Sony. It's a beast. Wii wins easily.