Achievements and stuff
Achievements on the 360 have changed what it means to 'complete' a game.
Even when the story has been finished with, there are often other things you can do to gain achievements which helps extend the life of the game.
There are some stupid achievements about, but on the whole it has been getting better as developers become more used to the concept.
It's fun to compare achievements with friends or to try and get the last few for a game. Games are about fun, so achievements are a good thing in my opinion.
Lets hope Sony do a decent job of it.
As regards the usual console flame war - I own an Xbox 360 and have yet to see any games on the PS3 that would make me want one of those instead. However, if I was recommending a console to someone who was new to 'next-gen' gaming then I would have to recommend the PS3. Some of the more current multiple format games like CoD4 and Burnout have been identical on both systems plus you get blu-ray and wifi straight out of the box with PS3.