Never cared for any of the PS2's stuff besides a few games, which admittedly MGS 2 is my favorite of all time. The only real great experiences I had on it besides that were Okami, which is an amazing, amazing game; something that would be on a top 10 list of all time for sure, Guitar Hero, which was cool, but was bested by Rock Band on the 360, and a couple other titles here or there.
I know this is late, and maybe a bit fanboyish, but I feel like all of what the Xbox had to offer felt more advanced, or just catered to what I liked more. Halo felt like something never been done before, and it still is the best thing in that franchise. KOTOR is still the best real-time RPG out there, and arguably one of the best RPG's of all time period. It was followed up with a great sequel, but more importantly, another masterpiece RPG in Jade Empire. Splinter Cell came out later on the PS2, but it felt gimped compared to what was on the Xbox. It was so fun, and really cool to see another take on the stealth genre besides MGS, and it worked flawlessly. Chaos Theory is all that needs to be said. Fable was a really creative and imaginative RPG, and yeah, it didn't live up to all of the hype, but I still lost countless hours to it. Don't even get me started on MVP Baseball 2005, or NFL 2K5, so damn fun. Rainbow Six felt like such an odd-game, but in a great way. It was so realistic for its time, but it was just so fun and addictive.
If you loved (W)RPG's and FPS's, the Xbox simply was the best thing on the market, and it's still probably my favorite system yet. Don't get me wrong, I love my 360, and my PS3, but the Xbox just hit on all cylinders for me. The controller, the branding, the games, just everything. It was great.