I own all 3 systems: PS3, 360, Wii. My 360 is now out of the 3 year warranty and I just got my 2nd Red Ring of Death. After getting it back the 1st Time, I started getting disc read errors.
The 360s harware problems are well documented.
It is true that Live is a litter better at getting you connected to friends, but it is not a show stopper in my opinion. PSN works really good and I have never seen any Lag. I also like that PSN supports more than 16 Players. XBox Live is typically 8, 16, and 24 max in most games. This is where you'll here the 360 fanboys tell you that 16 is the "Sweet Spot" that is XBot speek for justifying why we have to pay for XBox Live... Killzone 2 is awesome with 32 players in a match. Resistance 2 supports 60 players... I still prefer Killzone 2 however.
Since my 360 is so unreliable I mainly buy for my PS3. There are plenty of excellent games for both. I love Halo so that is all we use our 360 for anymore. As far as systems go I prefer my PS3 because it is reliable and I also love Little Big Planet and Killzone2 on the Exclusive fronts.