I prefer the Xbox because of the quantity of games available. If you don't count multi-platforms titles Gamecube probably have less than 20 decent games. (Mario Sunshine, Star Fox Assault, Twillight Princess, Wind Waker, Picmin 1 and 2, Metroid Prime 1 and 2, Mario Kart, Super Smash Bross, Eternal Darkness, F-Zero, Mario Golf and FF:CC). Those are really good games and many of them are better than any game on Xbox. Damn! Some of them are better than any game ever release till today. But other exclusives are not really good or only "ok" games (Luigi Mansion, 1080, Wave Race or Star Fox Adventures for exemple), not good enough to justify to buy a console.
Xbox was an awesome console with many many good games and a lot of exclusive titles : Arx Fatalis, Morrowind, JSRF, Amped 1 and 2, Rallisport Challenge 1 and 2, Fable, Forza, Halo 1 & 2, Jade Empire, Mech Assault 1 & 2, Ninja Gaiden, PGR 1 & 2 and many more). I don't know if you played Rallisport Challenge recently but theses 2 games are graphically OUTSTANDING even with today standards.
More importantly, for me anyway, Xbox has Xbox Live. At that time the one and only decent online gaming platform on a console. Let be honest, PS2 online service sucked. And Gamecube, aside of Phantasy Star, don't have any online titles.
I can't count how many hours I pass online on my Xbox playing Unreal Championship, Mech Assault and Return To Castle Wolfenstein chatting with my teammates. I still have many of the "friends" I made at that time in my Xbox One friendlist.
The original Xbox was the first console I bought by myself. Coming from the PC world, Xbox Live was a huge advantage in favor of the Xbox when came the time to choose a system. Next November, when the renewal will pass on my credit card, I will be a Xbox Live subscriber for 14 years, uninterrupted! So for sure Xbox has been a more significant console in my life than the Gamecube or any other Nintendo system to be honest (I was in the Genesis/Megadrive team)
So at your question my answer is : Xbox
;P