This isn't even a contest. The Wii crushes the Gamecube in nearly every conceivable way. I see a lot of nostalgia clouding people's judgement
Nearly every one of GC's big games has a far superior counterpoint on the Wii. Not only that but Nintendo had a much greater and more varied output on the Wii as well as better third party games.
Galaxy>Sunshine (2 Galaxy games!)
2d Mario> Nothing to compare!
DKCR> Donkey Konga?
2D platformers were pretty much nonexistent on the GC while Nintendo themselves made Mario, Wario, 2 Kirby games, and DKCR. People now act like 2d Mario has always been here but 2d games haven't been on consoles in any serious amount since the snes. You also had third parties like Boy and His Blob.
Sin and Punishment>Starfox Assault
MKwii>MKDD
Metroid Prime>Prime 3>>>>>Prime2 I only give the GC the win because is was the first and revived the franchise
Wii Sports games>Mario Sports games
Skyward Sword>Windwaker
EXCITE games>Wave Race
Red Steel 2>>>Geist
The c-stick was terrible for fps while the remote was the best solution a console has ever had. And it got fps from every Modern Warfare to Conduit 1 and 2.
Brawl>Melee unless you are tournament obsessed to insane degrees.
Monster Hunter> Nothing to compare
Xenoblade>Baiten Kaitos
Last Story
PUNCHOUT! Once again GC has nothing.
The return of lightgun games with HoD and the RE games.
That doesn't even get into all the fun niche and experimental games the Wii had.
Elebits- loved it and nothing else like it exists.
Rune Factory
Warioware
Muramasa
Little Kings Story
de Blob
No More Heroes 1 and 2
Madworld
Rhythm Heaven
Skylanders
Endless Ocean
Boomblox
Rockband
It also had games I could play with my family like Just Dance, Wii Fit and the already mentioned Wii Sports.
This is just off the top of my head too.
GC nostalgia case in point.
SS cuts corners by making us visit the same areas again and again. Oh and it was the guardians and thankfully WW had none of that chore BS.
WW had the most boring and loooong chore of a quest ever when it came to finding the triforce pieces. You even had to get money to pay to read them before fishing around the world. Nothing else comes close. When speaking of cutting corners it also had dungeons obviously entirely cut out.
A person who likes the GC output more than the Wii either has nostalgia goggles on or they hate motion controls to such a degree that it is more important to them than the Wii's superior lineup in all types of games.