I prefer my PS3 over the 360, and have done for a long time. Both systems are launch models (60GB PS3, 20GB 360), and I haven't had the RRoD (am I the only one?), though the 360 has thrown up E74 a few times which is resolved by a restart.
Game-wise there isn't much in it - most titles are multi-platform these days, and although the PS3 usually gets an inferior port, the actual difference isn't massive (well, except Ghostbusters...), and not enough to bother me (case in point, CoD: MW2 looks great on both systems). Both systems have some exclusives, but I've had more interest in the PS3 side of these (FF XIII Versus, LBP, Killzone, Uncharted, Wipeout HD, PixelJunk Monsters, Fat Princess) than the 360 (GoW, Halo, Fable). I'll play both systems, and buy exclusives, but if the title is cross-platform I'll pick up the PS3 release.
As for hardware, I much prefer the PS3. I can't stand the NXE, as I can't find what I want most of the time. It's basically a clunky, poorly designed UI. Sony's XMB on the other hand is elegant, easy to navigate and everything is where it should be. I also prefer the DualShock controllers over the 360's efforts - this may be due to being a PlayStation gamer since the original, but I've never liked the Xbox controllers that much.
I also appreciate being given WiFi, a user-expandable HDD and BD in the price. I had to fork out £55 for the 360's WiFi adapter, and the 20GB HDD is really restrictive now that games can be installed. I've stopped using the BD player in the PS3 as I have a pair of standalones, but it seems to evidence in the games (PS3 titles are noted for higher resolution textures) as well.
Both consoles handle streaming, but the 360 seems to demand Windows Media Centre. PS3 has iPlayer (fantastic) in the UK, which is seeing a lot of use.
I'll freely admit the 360 is a bargain. £125 for an entry point is great, but it is a crippled unit. If I was buying another 360 I'd be going for the Elite, and the PS3 is only £30ish more - but offers more. I can see the advantages for some people in the accessories being optional though.
Ultimately, just buy both. The prices have dropped so you can get two for what one originally cost, and then you get all the games and none of the fighting.