If you go on bungie.net, log in, and go to your character then click advisors, you'll see your raid progression as a bar fragmented into 8 sections: 4 for normal, 4 for hard. These represent the 4 drop points in the raid:
Completing the raid on hard mode first will give you double drop rolls, as you'll get a chance for drops from normal mode at the same time. You also get double drops from the left chest in the Gorgon maze, the only chest that drops in both difficulties. Basically, if you can complete hard mode, you don't even have to bother doing normal anymore and you get the same amount of loot as if you completed both.
It's also good to know, that the double rolls you get in hard mode will BOTH roll on hard mode gear, thus giving you a doubled chance to get the hard mode only weapons and helmets.
In addition, the loot table includes more things in hard mode that don't drop in normal mode, off the top of my head:
- Fatebringer (legendary, arc, hand cannon)
- Praedyths Timepiece (legendary, arc, pulse rifle)
- Praetorian Foil (legendary, solar, fusion rifle)
- Vex Mythoclast (exotic, primary, solar, fusion rifle, drops from Aetheon only)
- Raid helmets for all 3 classes (the legendary ones that max out at 30 light and drop from Aetheon only)
- Aspect of Glass (a ship)