Well the original XBox was better in a few ways, but not many
1 - Durability. That thing was a tank, and the only issue it had was the launch consoles that had power cord failures. Easy replacement by MS at free of charge.
2 - Best graphics on multi platform games. Before PS3 and 360 were evenly matched, the XBox had the sharpest looking games as long as it was on all platforms. Back then it was a pretty big advantage.
3 - Sega Love. Crazy Taxi 3, Shenmue 2 w/ Shenmue 1 movie, Jet Set Radio Future, Toe Jam and Earl, Outrun 2 (was out before coast to coast), Panzer Dragoon Orta and Spikeout Battle Street. All exclusives with the exception of Shenmue 2 but whatever.
Also had some pretty nice exclusives that I miss - Dungeons and Dragons Heroes, Grabbed by the Ghoulies, Kingdom Underfire Series (Thank God It's making It's true return soon), Oddworld: Stranger's Wrath, Phantom Dust (pure ownage!), Rallisport Challenge 2 (Best Rally game ever. Sorry Dirt.), Steel Battalian and Unreal Championship 2 amongst others. Also some good PC/360 exclusives like KOTOR and Jade Empire aka Amazing Western RPGs.
Oh, and Otogi 1+2. A shame Ninja Blade didn't turn out to be the return of Otogi.
For reference I own over 100+ original XBox games. I just haven't gotten around to adding all those games to my profile. They are on my IGN collection list.