Hulk: Ultimate Destruction is my favorite sandbox game of all time. That is because you play as the Hulk, and it feels like playing as the Hulk.

I like Crackdown a lot but it takes way, way, way too long to become comparable to the Hulk in that game, and it is just not crazy enough to stand next to its older brother.

So, if I were looking for a sandbox experience built around feeling powerful and being able to dynamically change the world around you, what should I pick up?

Keep in mind, the first of you who tries to sell me on a game because of its "story" or its "characters" is missing the point, here. In Hulk I could jump into the air, punch flying robots, throw them at other robots, surf on a bus, and then beat a giant robot to death with that same bus. Picking up and throwing tanks is par for the course. I could destroy entire city blocks with my rage. Mayhem on a scale that I have never managed to find again.

What sandbox game this gen compares in terms of variety, scale, and quality of mayhem caused?

I heard Prototype was almost an exact clone of it, you might to check it out...

Prototype is the game your looking for.

Prototype lets you karate kick helicopters, right?

The amount of restrictions you apply make it hard to suggest anything really.

As odd as it might seem, Bionic Commando is, I believe, the game that fits the best what you're looking for. The environment is not destructible, though.

inFamous does not let you interact that much with the environment but you can still glide and jump and slide and stuff.

Disclaimer: I have not played Prototype.

How is asking for mayhem a restriction, much less multiple restrictions?

Also, keep in mind that Prototype is made by the same developer so even if I haven't played the game, I'm pretty sure it must be similar gameplay wise.

" a sandbox experience built around feeling powerful and being able to dynamically change the world around you"

Multiple :P

That is not what restriction means!

from what I have heard you best bets would be Prototype, Just cause 2 and maybe Red Faction: Guerrilla and possibly the original Crysis. Thos I don't think any of them are exactly what you want they would probably be the closest games out there.