I always kinda appreciated niche games, and I was a big Dreamcast fan, so maybe I liked that niche element the system had going for it, while the mass market didn't. I've always tended to root for the underdog, and that was part of the appeal of the Xbox for me at the time. I have been discovering a few games now that I actually didn't play back in the day like Otogi 1 and 2, and I really want to play them, especially after learning they were made by From Software.
Even with many of it's great games being multiplatform though, it's already been mentioned, but many of them are better on the Xbox. Burnout games, Mercenaries, Splinter Cell...they all just look great on the Xbox compared to PS2. Even the games that did also come out on PC though, I've always been more of a console gamer, so if I want to go back and play KOTOR, I'll play the Xbox version because I personally can't stand the controls for the PC version. I need to have a controller in my hand for that type of game.