The new version obviously uses stereoscopic 3D effects to highlight the "3D-ness" of the world, but what else has changed for the 3DS release? Well, not much. The only difference I could clearly identify is in the color scheme. While the PSP game was deep, dark and moody, painting the world inside protagonist Danny's mind with subdued colors and nighttime skies, the 3DS game is vividly colorful.
This is a positive change, for a couple of reasons. First, the game isn't exactly menacing in tone; while the idea of insomniac Danny trapped in his own mind sounds dramatic, the storyline is delivered through jokey dialogue between Danny and the mad scientist who has induced this forced introspection. Second, and most importantly, the brighter, clearer look makes it easier to see your surroundings -- a good move for a game that is 100% environmental puzzles. The new graphics make it much more noticeable when you "crush" the level and go 2D; the shading and outlining on your character disappears, and you become an apparent 2D sprite (in a 2D bathrobe).
Wait, "crush" the level? I fear I may be losing the many people who haven't played Crush before. The central gimmick of Crush is that Danny navigates 3D levels, with a movable camera, and can at any time "crush" the level to make it 2D. Depending on the perspective, this makes a very different environment. For example, if you have one platform that is much higher than another one, you can view them from above and crush -- since the vertical dimension is now flat, you can walk from one to the other. Similarly, crushing from side view can allow Danny to jump from one platform to another, no matter how distant they may be in the "real" world, as long as they appear to be near each other.
Danny uses these abilities to cross otherwise impossible surroundings and find the exit, collecting the "marbles" he has apparently lost along the way (get it). You must collect a certain number of marbles to activate the exit -- additional marbles act as a challenge, as do "trophies" and other collectibles. Not that you really need the extra difficulty; I've found just figuring out how to get from one end of a stage to the other difficult enough, thanks to my foolish, three-dimensional brain.