Do you get better rewards for beating them on a higher difficulty or is it more like bragging rights
More like bragging rights, with two exceptions.
- Beating Easy, Medium AND Hard will unlock the ability to view the different weight stages freely in-game for that character.
- Beating Critical will unlock an extra scene in the Extras menu for that character.
Outside of those two unlocks, everything else will be unlocked for each character when you gain access to them.