Usually you go into "hard mode" by reading a book which makes the final boss fight harder. This is required for the gold key in some vet pledges. However, if you're just farming for a monster helm and not doing the pledge, is there any need to fight the boss in hard mode?
When farming vWGT I noticed that Molag Kena always drops 12 Daedric Embers, both in normal and hard mode. So I know there is no difference in the amount of trophies dropped.