I didn't get to play either until 2004; I'd been strictly PS2. The first of the two I played was the Xbox; my step brother had one but he didn't have much in terms of games....
GTA Trilogy, Conflict: Vietnam, WWF Raw and one other game which I can't recall. Obviously
WWF Raw was the only exclusive; I was a wrestling fan but that game was quite disappointing. I could see the graphics improvement over my PS2 but without experiencing any notable exclusives, it didn't really take my interest.
A few months later my friend returned from a trip to visit friends in England and he brought back with him an Xbox with
Halo: Combat Evolved, Elder Scrolls III: Morrowind, Rainbow Six 3 and a racing game which I can't recall. He'd played it at a friends and gotten hooked on
Halo; soon I was also hooked. We played the campaign on multiple difficulties and we'd spend hours having sniper duels on 'Blood Gulch'. Honestly at first we didn't really play much else on it; I remember trying
Morrowind but we weren't used to western RPGs so it seemed odd. He then picked up
Fable when it came out; great game, probably one of the first western RPGs I got into. I then remember when he picked up
Halo 2; I actually left an exam early to go to his house and play it; then we pulled an all nighter and finished it
Xmas 2004 I decided I wanted a new console; at first I considered getting an Xbox with
Halo, Halo 2 and
Fable. However for some reason i started to gravitate towards the Gamecube, which was odd really, I hadn't owned a Nintendo console since the SNES. And although I'd enjoyed a handful of N64 titles, it wasn't a console I'd really connected with. Nonetheless I picked up a Gamecube with
Mario Kart Double Dash, Pikmin, Pikmin 2, Sonic Adventure DX, Sonic Mega Collection and
The Legend of Zelda: The Wind Waker. Later I added
Final Fantasy Crystal Chronicles, Super Mario Sunshine and
Sonic Adventure 2.
Mario Kart Double Dash dominated the vast majority of my playing time for a long time; and I was scarily good as a result
.
Technically I never owned an Xbox but I did own a 360 later so could buy Xbox titles for that. So obviously I have been able to collect for both consoles since.
Xbox:Halo: Combat Evolved
Halo 2
Fable
Elder Scrolls: Morrowind
Knights of the Old Republic
Knights of the Old Republic II: The Sith Lords
Jade Empire
Deus Ex: Invisible WarGamecube:Mario Kart Double Dash
Super Smash Bros Melee
Final Fantasy Crystal Chronicles
Fire Emblem: Path of Radiance
Skies of Arcadia Legends
Metal Gear Solid: Twin Snakes
Star Wars Rogue Squadron II: Rogue Leader
Star Wars Rogue Squadron III: Rebel Strike
Pikmin
Pikmin 2
Super Mario SunshineThey'd be the must own titles for each system in my mind; however just because Gamecube has more, i wouldn't say it's necessarily better. So to be honest, my short answer is they're even, both worthy runners up to the dominant PS2