I had PS2 and GC, but not Xbox. In regards to Sega, the best thing about them going multiplat was being able to play Virtua Fighter 4 on a system that I already owned. VF4 and Evolution blew PS2-era Tekken out of the water. They were the best fighting games of the era.

I prefer Xbox. Jet Set Radio Future became one of my fave SEGA games ever and has one of the best OST's ever.  I also loved how you could burn CD's and games could have custom soundtracks. S controller was the best controller that gen. Of course I also got it for Shenmue II stayed for JSRF and Otogi 1-2. Panzer Dragoon Orta. Gunvalkyrie. Ninja Gaiden. Phantom Dust. I wish I could list Metal Wolf Chaos but it was stuck in Japan so I got to play it on PS4. Plus Xbox at the time felt like the closest thing to a continuation of Dreamcast for me. I like a number of games on Gamecube but dislike some other ones. Never liked that controller. Great hardware tho and a cool design. Just Xbox won me over. I did not have a PS2 until many years later.

I've never had either, but as a PC guy, I feel like this has to go to GameCube. I don't think there was that much going on for Xbox if you had a PC, and that was back when the difference between PC and console versions could be even more significant than today (and that's not to downplay the advantage PC has over consoles today).

Halo 1-2.
KOTOR.
Half-life 2.
Ninja Gaiden Black.
Jade Empire.
Fable.
Max payne.
Chronicles of Riddick.

Xbox wins.
Imho, easy win.

JSRF's soundtrack is burned into my brain. I don't own an OG Xbox right now because finding a working one in good condition is brutally hard. But once I get one I can't wait to jump back into JSRF just for the crazy soundtrack alone! Also, excellent picks overall for OG Xbox games!

Depends on your preferences honestly. For me, it's the GameCube, but the Xbox was cool, too.