The only SoT PoP i've played is the third one, so I couldn't give a good answer for it. A lot of the platforming, while very fluid, is also pretty automatic. I think you had to jump into a wall and then press a button to be able to wall run anywhere in SoT PoP. Here, you can run into the wall at a somewhat adjacent angle and he automatically runs down that way. There are a few things like rings to help extend your wall/roof runs by pressing a button. (B for me as I have the 360 version) There are also light plates where you need a specific powerup to use, and you can't enter certain areas until you have it. 2 of them are completely unoriginal and automatic, the other 2 have some sort of interactivity to it in its use.
Then there's the combat. I remember reading an interview that the developers didn't want to recycle the combat system SoT PoP had because it's been copied over and over, and so developed this 1 on 1 system instead. You won't run into a lot of enemies - usually in between different maps. There are also four bosses to fight in the game. The game is supposed to reward you by not being aggressive, instead being patient and waiting for the right moment to strike. However, it's too easy and somewhat boring - no longer are the days where you fight multiple enemies, you run up a wall and jump off it to land behind and kill one guy, turn around and kill the other one by swinging on a pole, etc. Now you just... shuffle back and forth, parry, attack, then rinse and repeat. Also, if you knock an enemy into a wall or edge, except for most bosses, you get an automatic kill, no matter how much health it had.
Oh yes, and someone mentioned this: you can't die. Where in SoT PoP where if you fall down a pit, you can manually reverse time as long as you had sand for it, Elika, the princess sidekick, automatically saves you from fall and puts you down on the last platform you were on. You can't die in combat either: should an enemy come down on you with a fatal strike, and you don't press the button indicated on the screen, Elika saves you, and the punishment is that the enemy regains health instead.
