I'm going to finally get myself a new console but only really for single player. I live on a boat so I've only got 3G internet so multiplayer is probably a waste of time. It sounds to me from reading about that the 360 is more online based and the ps3 less so, although either way I'm probably missing out. Its going on a 26inch tv which only does 720p. I like racing and football games, and the odd fps. Not a big fan of fantasy stuff though. I've got a small pile of original xbox games, but then again I've still got the xbox. If I got the 360 I'd get an elite, which aren't much less than a ps3. I'm swaying towards the PS3 at the moment, would be nice to have some sort of blue-ray player. Sony sound like they are less likely to replace it soon as well. There's always the wife acceptance factor as well. Is one or the other better for games that she won't hate? What would you do?
Look at the games (that I will talk about) and decide yourself. Basically they both have a lot of good exclusive single player games but 360 is a lot better for the traditionally hardcore genre's (FPS, fighting, RPG etc.) whereas PS3 gets more unique stuff like strategy RPG, Heavy rain, LBP etc.
The only exclusive fighting game is on 360. Dead or alive 4 and it's very good acually, one of the best animated and quickest fighting games around with a good roster and well balanced fighting system.
Racing I'd give it to PS3, Motorstorm is very fun and while I like Project gotham racing and Forza the PS3 also has the wipeout HD game and GT5 coming (basically winning because it's racers are a bit more varied and it's 3 to 2).
Shooter wise (third person and second person) it's hard to call and I'd say go with which you prefer. I personally like sci-fi a lot so 360 having Mass effect and Halo is great not to mention it has Gears of war which is a great series. PS3 tends to have more titles in the shooter genre but games like Killzone and M.A.G. are not quite as iconic and well done as gears or Halo in my opinion. Uncharted is very well done but I found it a bit over rated to be honest.
Action games PS3 wins, Ninja gaiden sigma 2, Heavenly sword and God of war 3 are both great games and worth playing.
RPG wise unless your into playing strategy RPG PS3 falls on it's back with 360 thrashing it. Demons souls and Valkyria chronicles are good but compare it to Lost odyssey, Tales of vesperia (not out in europe or America on PS3), Magna carta 2, Blue dragon, Fable 2 and the Mass effect games and the PS3 has much less to offer. This is just my personal experience but I found that the strat RPG's got tiring, I played Disgaea 1 and 2 for hundreds of hours but you can't do it again and again and again without tedium setting in.
So for me it's 3 to 2 in favour of 360. Maybe if you looked at other genre you'd get different scores but basically they are both very good consoles and have lots to offer, as a single player console try and think what you prefer in a more cinematic focused game or more gameplay focused ones. It's my opinion that the PS3 is becoming over cinematic and focusing too much on graphics while missing out on gameplay in some titles. Not all but basically Sony wows people with graphics at the moment (not saying they don't have good titles but a lot of the hype for some of there titles is based on graphics).