I'm going to try to keep this short and on point since you and Vivi got through a lot of it.
I can just ask - how many of those games have you actually played? I would absolutely say God of War is different - not just with the stuff going on in the scene, but an item system, weapon diversity, ways to manipulate enemies, and overall deeper combat which the series simply didn't have. A Gran Turismo demo/contest was released on PSN which showcased the new driving physics, and for a game which prided itself on realistic driving for over a decade, it did feel very different. Not to mention cockpit view which you will be able too look around with using the EyeToy
I can't comment on the 360, but there's been a lot of innovation on the PS3 among, but definitely within genres. MAG didn't just increase the player count, we've "finally achieved real time battlefield control..." (<- SNAKE!) with a tiered leadership infrastructure. Demon's Souls undoubtedly innovated the Action-RPG genre with the use of Havok physics but moreoso online play I haven't really seen anywhere else. Valkyira Chronicles did something for SRPG's which is a wonder it hasn't before. LBP's combination of an in-game editor and community incorporation of it in-game and out-of-it created something genuinely new.
We could even go into FPS like Bad Company 2 deconstructing the entire concept of the action set piece, or how Killzone 2 really changed how I think about FPS. I've been on BC2, MW2, and MAG lately, but going back to Killzone 2 was a painful experience because it plays so differently, it's something that hasn't been done before and it could not have been done without greater processing power of the PS3.
And while you said Heavy Rain is just like the old point-and-click adventures (it is) it's also similar to many different things, it's hard to say exactly what it is.
Have you played Valkyria Chronicles, Demon's Souls and Heavy Rain? If you have I'd really like to know your thoughts on them, just in general, but also for the sake of this thread.