Are there any incentives to climb on stuff besides the fact that I can?
In the game you do a series of missions and in most of those mission you choose if you are going to help the people with your super powers or you use those powers to do bad stuff to the city and scare people. And whatever you did in the first game, is going to carry over to the sequel.
Also, the story can be a little hard to follow at times, but in the end, you will put more attention to the characters and/or the gameplay itself to be honest.
...and with out throwing to much spoilers that's the game. Is great game, though, it can get a little repetitive if you play it in long sessions but is still a lot fun.