The classes this far in early access do not have a lot of distinguishing abilities (yet).
There's 2 portraits with different coloured clothing available per class.

It's wise to collect different fears per class so you can build a team however you like farming whichever you need.

Each class has the same default value with a class specific bonus:
3HP, 2 Speed, 5 items (1 headgear, 1 Torso, 1 Footwear, 1 Pocket item, 1 Weapon)

Currently the classes specific stats are based on weapon and class-buff only: