Crysis vs. Unreal Tournament 3 (UT3), there are many discussions on this topic; I have no means to pretend to be the “game expert” here. Since I am a First Person Shooting (FPS) game fan, I intend to share my opinions via this blog. I find many debates over this issue started on the wrong foot because this is really a personal preference. Therefore, I’d like to lay down my FPS gaming experience first so you know where I am coming from:
My first FPS game was the good old legendary Wolfenstein 3D, then I picked up Doom, then the Quake Series. During Quake II, I stopped playing the story line based FPS and moved on to multi-player FPS games. Quake II Mod-Rocket Arena (RA) was a solid starting point. I got really “sucked in” by the Quake III Arena Mod - Rocket Arena III – practicing rocket jumps and rail gun shots on Friday nights. After my RA clan dissolved, I started playing Counter Strike and Days of Defeat which are the MODs of Half Life. Then of course, that got migrated to CS Source and DOD Source (both are based on the Half Life 2 game engine). In between Quake III and CS, I also tried the Unreal Series: Unreal Tournament 2, UT 2004, and then UT 2005. I have also played Far Cry and F.E.A.R. My most recent attempt in FPS is Crysis and UT3. Yeah, in the meanwhile, I did graduate from high school and got into university and later on got a job.
Alright, now you know what I have played, here’s my opinion on these two games: I think Crysis is the winner simply because the game has changed the FPS dynamics not simply from the graphic and sound aspects as all the other games do (UT3 included). It has changed the gaming experiences by introducing new elements into the combat. Started from In UT 2004 and Battlefield 2, players can drive vehicles or airplanes; but starting in Crysis, players can modify the avatar’s speed, armor and visibility in the middle of a shoot off, which makes the game much more complex and fun. Although the whole “wheel menu” UI and "suit mode" remind me of the console games. On the other hand, I felt that Unreal Tournament 3 is just another UT game, the same old gameplay, nothing new really.
When it comes to FPS games, you can't ignore the graphic comparison, although I say it really depends on the hardware and other elements, but here are some side-by-side comparisons:

Cleary Crysis win this one, well, if you are only looking at "human" skin textures that is... There are lots of detail in the people and very dynamic facial expressions "grabbing the neck faces"...

The physics between the two games are quite different since Crysis is aiming more at the real world battle simulations and Unreal Tournament 3 is aiming at the Sci-Fi “hover boards” style physics. Both are doing it well I think. But I still appreciate more on the running and gunning
effects in Crysis, with some nice blur effect.

Weapons and Firing, since UT3 weapons are more built for science fiction, the fire effects are fancier than Crysis. E.g. Using the “Shock Gun” to shoot the light balls out and then use the beam to nail them for a wider range explosions, you can almost feel the air vibrates around you when you do that, really cool!

Plants comparison, well, not much need to say here, Crysis is a clear winner. Where the palm trees are so pretty you hesitate when you shoot in the woods because your bullets will break them apart...

Avatar comaprison, both are well done, but I think the "power suit" in Crysis is the best looking amour ever.

Lighting comparison, The Cry Engine is simply built for out-door natural light settings. It has the best lighting effects among all the FPS games I have played so far...

Both games have improved their graphics incredibly but I am still impressed more by the Cryengine 2 renderings. I found that some texture rendering in Crysis are purposely blurred to add effects and decrease processor demand. This is really neat when you have lower end machines. When I lowered the graphic settings down on both games, I experience that Crysis is a bit more playable than UT, but of course this really depends on the hardware settings. (FYI, I am using a Dell XPS laptop with the Geforce Go 7950 GTX graphic card)
In comparison to CS Source (Half Life 2), the game settings in Crysis are much more complex, maybe even a little unnecessary according to some players. Many FPS fans may complain that the fancy objects in Crysis (trees, burning cans, and metal fences) are overkill in a game, well, true, but I think this make the game more realistic?
I also find the shadowing effects are not as sharp as in Crysis, say in the “Under City” level. Anyway, in conclusion, I value the gameplay in Crysis a lot. The “add-on” effects to the avatar by the “maximum strength” of the suit are just revolutionary. UT3 is a wonderful game too but it’s nothing like Crysis. HOWEVER, I believe UT3 will have a slightly bigger players community because there are way more documentations and video tutorials out there for the game modifiers than Crysis.
Ironically, neither of the two games are sold well in the past couple of months, they are both losers in comparison to Team Fortress 2 based on the box offices. Reasons? Same as I stated in the beginning, TF2 focus even more on game tactics and character buildings. Darn, looks like I am going back to the Source-based games...
PS-I am also a Real Time Strategy (RTS) game fan, well more like the "Blizzard" fan: Diablo II, Warcraft II, Starcraft, Warcraft III, Startcraft II(coming...). Well, there ought to be another confession I suppose...
PS2-Oh, yeah, my Massively Multi-player Online (MMO) game friends somehow read my blog and complained the still-not-completed-confession: Chuanqi (Legend, one of the earliest Chinese MMO game), WOW and EVE... If I ever get to them...