The Mechromancer is best described as a young adult who created a death robot that goes around slashing people's faces. Her skills are very different in the respect that it's a give/take type playstyle (in that while it benefits you in one way, it has a negative effect as well). They focus on supporting herself and her deathtrap (robot that slashes people's faces), the elements and damage output (at the cost of accuracy).
Psycho class is basically just that. You play as one of the badguys who has an inner voice which keeps in line with the good guys. You'll hear funny things such as "(Now say thank you) NIPPLE SALADS (close enough)" while you're playing. Plays much like Brick in terms of his main ability short of the fact that you can also throw the buzzsaw around like the badass psychos that exist in the game. His skills range from self damaging for personal gain, to making your melee devastating and naturally, your gun efficiency hilarious
EDIT: Also, who has a headset for voice chat and who doesn't?