Depends on what you are looking for really.
The Xbox console advantages were the built-in HDD, online gaming, custom soundtracks and best-in-class graphics.
The Gamecube console advantages were the GameBoy Advance Player and Wavebird controller. It was also no slouch in graphics.
The Xbox had quite a few solid exclusives. Halo, Dead or Alive, Forza, Project Gotham Racing, Voodoo Vince and the Otogi games were standouts for me.
The Gamecube had a solid lineup of exclusives. Mario, Zelda, Metroid, Luigi's Mansion, Starfox, etc. And who can forget the unforgettable Rouge Leader? You got to make the mother-F'in Deathstar trench run!
I own and/or have owned both. It's hard for me to pick a favorite because both were so different and unique. If I had to pick the one I played the most, it would be the Xbox. I cannot tell you how many hours I dumped into Halo and Project Gotham Racing on that console. On the same token, I had more frustration with Xbox than the Gamecube. While my Gamecube ran flawlessly every single time I used it, I went through several Xbox units because of HDD errors, dirty disc errors, etc. I had bad luck with Xbox hardware and atrocious luck with 360 hardware. Hence, why I won't buy an Xbox One.