I have both and dont really have any bias towards either so i'll list off what i find useful about both.
PS3 - Can play PS1 games no matter which version you buy, 60GB ones with the card reader etc can play PS2 games aswell which was then removed in the 40GB's and any new consoles since. If you're only after playing games with no interest in the social side then i'd go PS3. Sony has a lot of decent first party studios bringing out exclusive games whilst also getting multi-platform games too so you're never gonna be stuck for something to play. PS3 doesn't have that many third party apps though, only 4OD, iPlayer, ITVPlayer, Netflix and Lovefilm off the top of my head.
360 - The daddy of online gaming. Party chats incredibly useful so you can talk to your mates constantly even when playing different games. Solid first party games like Forza, Gears etc but there doesn't tend to be that many with only their big games releasing now and again. 360 imo is also the better console when it comes multi-platform games and they nearly always seem to play better on 360, not saying this is fact just something i've noticed with a lot of games i've played on both consoles (Skyrim being a case in point, ran like shit on PS3 at launch whilst being fine on 360). Onto apps, 360 is brimming with them now, Netflix, Lovefilm, iPlayer, Twitter, Facebook, Vevo etc its got the lot and they work brilliantly, i never thought id use them much but i seem to use them daily now. Also, people moan about paying for live but if you phone MS you can always get the price down to around £24 for 12 months :)
As for graphics, you'll be hard pushed to notice any difference between the two consoles as they're both pretty much neck an neck in that department.