Than I would suggest the XBOX 360.
Having played a varied range of FPS titles on both consoles and I feel that this genre plays better on the XBOX. I can't quantify it but for me the 360 controller seems better suited to the task. (If you said fighting games like Street fighter I would have recommended the PS3. The SONY controller is far superior to the XBOX one in this genre.)
XBOX boasts the largest online community, but there is a catch here as while the PS3 is free to play online, the XBOX has a monthly, 3 monthly or yearly subscription fee.
While paying to play does suck, the trade off is that the XBOX live system has been more stable, has better voice communication and the majority of downloads don't take any where near the times experienced on the PSN.
There are also currently a wider selection of FPS games on the 360, with some exclusive title having a large and very active online community; HALO 3 (FPS) and Gears of War II (Third person shooter). The major cross platform titles like the Call of Duty and Tom Clancy games also have large communities.
Just to be fair though (and hopefully not add confusion to your choice), the PS3 does have a couple of FPS games with large communities; Resistance Fall of Man 2, Killzone 2 (FPS) and SOCOM (Third person shooter).
So you won't miss out which ever console you pick .... (Just pick the 360