I think it depends on if your using the xbox or PC. Personally, I don't have/use xbox live, so I use the PC for all online - so, I don't what can/can't be done for the xbox.
Firstly, lag - I don't get much myself, although there are a few bad servers.
Maps - on the PC edition, alot of people are creating custom maps (varying in quality, admittly, but there are some great maps there)
Now, Halo I didn't like (never played online so can't compare them on that front), CoD 4 is an excellent shooter, and BF2 (I do like BF 2142 as well, but it seems alot of players don't). However, TF2 I like for its simplicity, great stylised graphics, and the high level of balancing (again, aside from some of the custom maps)
------------------------------------
For Queen and country, old clap....
Ok, I don't really talk like that, but I had you going, no?