What effect does difficulty have on the console version of Diablo 3?

There's a blue post over at the official forums trying to clear up some of the confusion. Essentially, those modes (Easy, Normal, Hard) do not alter Magic Find, Gold Find, and XP bonus in any way. They're just there for players to adjust the difficulty to their liking, increasing monster hit points and damage.

The Master I to Master V difficulties are different though:

• Master I: +60% Magic Find, +60% Gold Find, +120% XP Bonus
• Master II: +70% Magic Find, +70% Gold Find, +140% XP Bonus
• Master III: +80% Magic Find, +80% Gold Find, +160% XP Bonus
• Master IV: +90% Magic Find, +90% Gold Find, +180% XP Bonus
• Master V: +100% Magic Find, +100% Gold Find, +200% XP Bonus

That's pretty much the gist of it.

You need to hit level 10 to have access to the Master options.