well I own PS2, and my friend has an X box. I mainly play outlaw golf, mech assault and ghost recon. (i get lazy about capital letters sorry).
Personally I am not a fanboy of any system, i am just a fan of a good game on any system. So if you want to take into consideration how many "good games" PS2 has compared to X box, lets take a look here:
Here's a list of games from IGN.com for PS2 rated 9 or above on a 1-10 scale: (don't mind the buy now thing)
game title --genre-- score
Gran Turismo 3 A-spec Racing Buy Now 9.8
Grand Theft Auto: Vice City Action Buy Now 9.7
Metal Gear Solid 2: Sons of Liberty Adventure Buy Now 9.7
Tony Hawk's Pro Skater 3 Extreme Sports Buy Now 9.7
Devil May Cry Action Buy Now 9.6
Grand Theft Auto III Action Buy Now 9.6
Twisted Metal: Black Action Buy Now 9.6
Final Fantasy X RPG Buy Now 9.5
Aggressive Inline Extreme Sports 9.4
Baldur's Gate: Dark Alliance Action RPG Buy Now 9.4
ICO Adventure Buy Now 9.4
Jak and Daxter: The Precursor Legacy Platform Buy Now 9.4
SSX Tricky Sports Buy Now 9.4
Suikoden III RPG 9.4
Tekken 4 Fighting Buy Now 9.4
DDRMAX: Dance Dance Revolution Music Buy Now 9.3
NBA Street Sports Buy Now 9.3
Pro Race Driver (UK: TOCA Race Driver) Racing Simulation Buy Now 9.3
SSX Sports Buy Now 9.3
Tony Hawk's Pro Skater 4 Extreme Sports Buy Now 9.3
Virtua Fighter 4 Fighting Buy Now 9.3
World Soccer Winning Eleven 6 International Sports 9.3
Klonoa 2: Lunatea's Veil Platform 9.2
Madden NFL 2002 Sports Buy Now 9.2
Maximo: Ghosts to Glory Action Platform Buy Now 9.2
NFL 2K3 Sports Buy Now 9.2
NHL 2002 Sports Buy Now 9.2
Ratchet and Clank Action Platform Buy Now 9.2
Red Faction II First-Person Shooter Buy Now 9.2
TimeSplitters 2 First-Person Shooter Buy Now 9.2
Ace Combat 4: Shattered Skies Shooter 9.1
Half-Life Action 9.1
Madden NFL 2003 Sports Buy Now 9.1
Red Faction First-Person Shooter Buy Now 9.1
ATV Offroad Fury 2 Racing Buy Now 9.0
Burnout 2: Point of Impact Racing Buy Now 9.0
FIFA 2001 Major League Soccer Sports 9.0
Frequency Music Buy Now 9.0
Kingdom Hearts RPG Buy Now 9.0
Madden NFL 2001 Sports Buy Now 9.0
NCAA Football 2002 Sports Buy Now 9.0
Need for Speed: Hot Pursuit 2 Racing Buy Now 9.0
NFL 2K2 Sports Buy Now 9.0
Silent Hill 2 Adventure Buy Now 9.0
Sky Odyssey Simulation Buy Now 9.0
Soul Reaver 2 Adventure 9.0
Star Wars Jedi Starfighter Flight Action Buy Now 9.0
Star Wars: Starfighter Action 9.0
Tekken 4 Fighting Buy Now 9.0
WipEout Fusion Action Racing Buy Now 9.0
Now here's the listing for X box:
game title genre score
Halo First-Person Shooter Buy Now 9.7
Splinter Cell Third-Person Action Buy Now 9.6
Tony Hawk's Pro Skater 3 Extreme Sports 9.5
Dead or Alive 3 Fighting Buy Now 9.4
Elder Scrolls III: Morrowind RPG 9.4
Deathrow Sports 9.3
MechAssault Action Shooter Buy Now 9.2
RalliSport Challenge Racing 9.2
Unreal Championship First-Person Shooter Buy Now 9.2
Aggressive Inline Extreme Sports Buy Now 9.1
Jet Set Radio Future Extreme Sports 9.1
NFL 2K3 Sports Buy Now 9.1
TimeSplitters 2 Action Buy Now 9.1
WWF Raw Wrestling Buy Now 9.1
GUNVALKYRIE Third-Person Action Buy Now 9.0
Metal Gear Solid 2: Substance Action Simulation Buy Now 9.0
NHL 2002 Sports 9.0
SSX Tricky Sports 9.0
Tony Hawk's Pro Skater 4 Extreme Sports Buy Now 9.0
World Series Baseball Sports Buy Now 9.0
Wreckless: The Yakuza Missions Action 9.0
PS2 has a bigger selection of "better" games by far. Now you have to look and see what those games are comprised of. Nearly half of x box's best are sports. The rest of the field seems spread out with action and adventure.
About 1/3 of the top 50 PS2 games are also sports. The rest are mainly action and adventure also.
Now, as for the "almost great games", those rating 8.0-8.9, X box has a giant library of 60 titles in that range, while PS2 comes in with a mega whopping thunderous 116 titles.
When it comes down to it, PS2 definately has more bang for the buck. But of course, you're most likely not going to be playing ALL of those games. So you have to decide what games you like and which system has more of them. Many games are now multi platform so you need to take that into consideration also. Then there's the online aspect. PS2 needs a seperate adapter for 40 bucks to play online. It also supports 56k dialup whereas Xbox live doesn't. Last but not least, you need to think about the interface of the games. i personally cannot stand the xbox controller at all and have a hard time trying to adapt to it. Even with my big hands it's a royal pain in the ass. the S type controller (smaller version) is definately more put together, but the buttons are still just as user unfriendly as the normal versions, as you have to make twice the amount of effort to push in one of them as you would a PS2 button.
Plus, you might also take into consideration the ease of which you can play "backup" games on the system. X box requires a mod chip and you need a dvd writer, and dvdr's are expensive, as is the media. PS2 can play backups with a no-solder mod chip plus a boot disk combo all for 35 bucks. Backups can be had online for very cheap if you look hard enough.
As for now, I firmly believe PS2 has all the bases covered.