Ok. Here's my opinion, though I've not played them all.
Halo 3.
Simply because it has the best controls ('bumper jumper'), is the most dramatically cinematic both visually and aurally and has the Forge. On the downside most of the people who play it are racist pipsqueaks and it is actually light relief if one of them is tunelessly singing as if they think they are playing Singstar. I have found this to be such a problem that I purchased a wireless headset solely so that I could route all chat through it and then deliberately not wear it - this is because I have better things to do than individually mute fifteen players in Big Team Battle.
I play Call of Duty 4, but find the colour scheme rather depressing. The controls are a total disaster, so much so that I have taken to using a partially left-handed arrangement - so you hold the 360's right thumbstick to sprint, aim with the right trigger (yuk) and fire with the left (double yuk). I don't like crouch being on a separate face button rather than on the left thumbstick as I can't "hold to crouch" as I can with Halo. Strangely, I much preferred the Campaign in COD4 to that in Halo 3; but then COD2 had been much better than Halo 2. For some strange reason the lobbies in COD4 are comparatively well-behaved, but as no one seems to act as a team 'in game' my headset remains unused.
Gears of War got taken back to the shop, I don't understand how people can say it has the best graphics when I can't tell each side apart, or when they say it has the best strategy (cover system, roadie run, flanking maneuvers) when I can't see what I'm shooting at as it is grey on grey with my super-enormous body in the way and my equally brutish gun is surprisingly ineffective unless I get close enough to rip through their exoskeleton with a mini-chainsaw that produces gouts of something that is almost, but not quite, entirely unlike blood.
I gave the Battlefield: Bad Company multiplayer a go, but wasn't that impressed. After all, if you can break through most walls (but note, not any ceilings...) you tend to bugger the topology of the gameplay - that is, where you can physically get to from any point on the map, in other words the semi-contrived routes, pressure points and dependable cover spots designed by DICE (it is like playing CHESS, but allowing all pieces to move like a Queen).
I couldn't abide Team Fortress 2. I seemed to wait an eternity to join the match arena, then died almost instantly. The learning curve was too steep. I also felt misled and was disappointed that it wasn't fly-on-the-wall third person, or an intelligent floating camera like Zelda.
Unreal Tournament and Quake are too fast for me. I bought Quake Wars (looked promising) and found it to be the worst game I have ever played, so that went back to the shop.
If I could play any online shooter, money no object, that I don't already, I think it would be Crysis. From the footage I've seen it looks like it plays okay and you can use a 360 gamepad with it, but I would need a much, much, better Macintosh and I can't justify the expense.