I didn't know about this until I went to a friend's to play Rocb Band 3. I have PS3, he has X360.
On the PS3, any local player can unlock trophies. But when my mate & I were playing RB3 on his X360, I fulfilled certain criteria and failed to unlock the corresponding achievement, which I thought was weird. Until he told me how the X360 system works.
There are pros & cons to both systems. The PS3... any local play can get trophies. But you can't have more than one PSN logged into a game... which is something you can do on the X360.
Personally I think the X360 has the slight advantage in that you can have 4 players all logged into, say, RB3, and all of you unlocking individual achievements on your own accounts.