Both systems offer good FPS games. The 360 has Halo 3 and Bioshock, while the PS3 has Resistance, Warhawk (Not an FPS, but you should enjoy it the same. You might love the game, actually), Haze (might be decent enough). Both have (or will have) CoD 4, The Orange Box, etc. So, for FPS games, you can't go wrong either way.
Honestly, I'd prefer Resistance and Warhawk over Halo 3 and Bioshock. No offense to the Live people, but I am not enjoying my Halo 3 online experience. Too laggy, too long to get into games, no dedicated servers, etc. Plus, none of my friends own 360s. The PSN has always been relatively lag free for me, plus every online game I've played (limited selection, though) has had good dedicated servers. Plus, it's free (Hey, it does what I want...I grew up playing games online on the PC! The PSN works for me ). Yeah, Live doesn't cost much, though. I just can't bring myself to play Halo 3 over Warhawk (especially with the ranking system fixed). I just have more fun with my PS3. It just feels better, more smooth to me (especially the PSN, regardless of how little it may offer compared to Live).
I also just prefer games associated with the Playstation consoles. It really comes down to personal preference. What games do you want? If you want Bioshock, you may be better with a 360. Just look at what is out and what will be coming out. Figure out which one you think you'll have more fun with. It's all personal preference.
But, since you asked, I'd say PS3. I simply enjoy it and the games more than my 360, and that's all.