The difference between the PlayStation Vita version and the console versions is small.
With the lack of multiplayer, they added in a Ghost mode. You also have relics to find, which use the touch screen to grab in the environments. You know they're around when you hear a certain sound, the tutorial levels will make the sound clear. The relics unlock pieces to murals that were added to the game in this version.
The visuals are really great on the PSVita's OLED screen. Nice and vibrant, the game has never looked better. You can pinch in/out to zoom in/out, which lets you look at the game's visuals up close and personal.
That's the only differences, well and it being portable. Which has it's own value to some. The game itself is fantastic. It can be difficult at times, but it's one of the best 2D platformers made this generation. With plenty of unlockables and things to earn.
The gameplay is the same as the console versions, with the exception of the pinch in/out and touching relics mentioned early. The core gameplay is exactly the same. And it controls wonderfully.