I think fundamentally they target their audiences in different ways, meaning both consoles appeal to difference people for different reasons.
If we ignore 'exclusives' for a moment, then the 360 and PS3 can deliver quite different experiences, depending on you.
360 wise, for me..
I switch my console on, play a game, at random intervals, mates drop on, and I'll invite/be invited to chat with them, at some point I will either jump into a MP game they are in, or we'll agree to start a new MP game, and someone will 'invite' the rest of us in.. The key on the 360 is, I'm able to maximise my gaming time because I can be playing whatever I want, whenever, and still interact on all levels with my mates..
PS3 for me,
As can be seen from the 360 experience, I have to change my usage, I switch on, play a game, then start 'phoning' people, or keep periodically popping out of the game when I know people have just popped on. And coordinating a MP game for 6 or 8 people ranges from a pain in the ass to almost impossible.. Which ever way it's spun, I just can't be playing games as much of the time, and although in isolation most inconveniences are trivial, for me, they stack up to make it noticeable more awkward to use the PS3 then the 360.
It doesn't mean I hate the PS3, I just much prefer the 360 experience. I realise both have exclusives etc, and so never really comment on those, that's another personal preference issue as far as I am concerned.
Then if you look at where they are heading, you have the 360, building on it's 'intergrated' feature pack, allowing even more social interoperability whilst gaming..
Sony are persuing HOME, a much more socially rich environment, but still fundamentally lacking in it's integration with the XMB whilst gaming. Sony have 'promised' some enhancements to the XMB to address this, but it's still no where near the 360 level.
To me, I can see how different people are going to gel differently with each console, and also how they are quite opposed in their experiences, leading to a much more heated debate.
There are other aspects as well, the 360 hardware failures have tarnished the 360, despite being very reliable now, this stigma isn't going to go away.