You do earn more. The bonus of the difficulty will apply to the souls and gold. The main problem with it is that if you play one PvP on a lower difficulty, it overrides all your work for the week. Winning every match on Warlord 2 for a week currently gives you +75% souls and +50% gold of you rank reward.
The reward system should be expanded more for higher difficulties as well as averaging the total of the difficulties used, such as:
normal = 1
hard = 1.5
Warlord 1: 2
So someone who plays 20 warlord 1, but then 10 normal difficulty, would get a weekly reward of 1.67x their rank reward. Someone who did all Warlord 2 would be 2.5x, all Warlord 4 4x, etc.