Some of the character skins have special abilities. For example, there are masters of Psi powers such as Barret, Pyro, and Lenov. They can do many more things than Nick with their powers. If you were to unlock their skins, you will also get those abilities.

Edgar Barret: Can carry all MPs, has the ability to carry very heavy objects (boxcars, trains, crates, etc.; preferably in the Barret boss fight), Psi drains slower than usual.
Jov Lenov: Can Mind Control anyone, can make anyone commit suicide at anytime, Psi drains slower than usual.
Marlena Pyro Skin: Her Pyrokinesis can burn faster, fire goes through most objects or until it hits a wall, Psi drains slower.
The General Skin: Has all the powers listed above.