To quote Bit Kid from the Steam community forums:

• Thieves are faster, much higher starting LCK but lower other stats, 100% crit rate for backstabs, Knife weapon damage boosted, start with Knife
• Mages have much larger starting Mana pool and INT stat, Mana refilled at save points, very bad with melee weapons (0 starting STR), higher chance for mana drop from hanging lights and enemies, start with Magic Knife spell
• Warriors are bad at the arcane arts, but can swing melee weapons faster, STR increases faster than other stats

How should these factor in to the various categories? Should we not use classes?

Thief moves 15% faster, but I don't know if that applies to backdashing or slides as of yet.

More damage from Warrior str scaling might make bosses a bit faster, but going fast doesn't tend to allow for much leveling up.

Mage also seems interesting, but the 0 starting strength hurts a lot.

And a point for not using them for now: they also might be changed in the future, and as an example: the Bit Kid account has expressed interest in making the mage backdash a short range teleport.