Xbox 360
Pro's
More games
Xbox Live - cross game chat - talk to friends online regardless of what game they're playing.
Xbox Live - more people online, more AUDIO chat as all units come with a microphone headset
Cheaper initial purchase price
Installs are optional - not mandatory
Ability to play your own music in game
Xbox backward compatibility
Multiplatform games generally look a smidgen better on the 360.
Cons
More wires due to external power supply (hardly a big deal)
Xbox Live - it's not free
Xbox Live - more kids swearing & cursing online as all units come with a microphone headset
Hard drive is microsoft proprietary & costs more + you can currently only go to 120GB
Batteres for controller or having to buy a charge & play pack
No Built in Wi-Fi - Microsoft external Wi-Fi add-on is expensive
No Blu-Ray - external HD-DVD is pretty much a dead format & no use for games.
DVD drive is noisy - optional installs solves this problem for games
Unit is noisy (new ones are quieter)
History of unreliability (new Jasper units are apparently a lot better, but only time will tell on this).
PS3
Pros
Quiet
Reliable
Built in Blu-Ray drive - plays Blu-Ray movies, upscales DVD's - 50GB storage for games as opposed to 9GB on the 360's DVD drive
Internet Browser - it's not as good as IE8 or Firefox, but it's usable
Built in rechargable batteries in controller - just plug into USB socket on PS3 using supplied cable.
Built in W-Fi
Standard 2.5" 5400rpm laptop hard drive installed - can upgrade without voiding warranty very cheaply - Sony even supplies instructions for this.
Built in PSU so less wires (one to TV, one to mains supply).
PSN Network & Online play is completely free
Less kids screaming abuse over microphones as PS3 doesn't come with a mic headset.
Exclusive games are the best looking games out there, & the upcoming titles for late 2009, early 2010 are looking amazing.
PS1 backwards compatibility (see Cons about PS2 compatibility).
Cons
Less games than 360 but still plenty
No Cross game chat - you can only talk on a microphone to people playing the same game as you or on the XMB
More expensive initial purchase price
Less Audio Chat as PS3 does not come with mic headset
Multiplatform games are generally a smidgen inferior on the PS3 due to development issues & iffy porting techniques.
Mandatory Installs - having to wait anything from 2-15 minutes before being able to start a game (every PS3 comes with a hard drive so developers use it as it's got faster access times than Blu-Ray).
Only 2nd hand older PS3's have PS2 backwards compatibility.
Can only play your own music in game if developers put that facility in - on a game by game basis.
In the end it depends on what games you want to play?
With regards to Hunters comment about the 360 being the number 1 selling platform. Sorry, it's not. The Wii has sold nearly as many units as the 360 & PS3 combined - doesn't make it better, just more popular.