How to change the form of Deoxys in Pokémon X and Y

Having completed the game and done much of the postgame stuff, I belive I can say with a fair degree of confidence that no there is no different difficulty setting.

They're awarded by your friends (or, I believe, passers-by) pokemon (those left in Pokemon Amie). They appear to come most frequently when you sit idle at the Pokemon Amie screen, and will continue to be given if you just sit there while doing nothing at all. The item given appears to be random, but it will always either be a cosmetic item used to decorate the Pokemon Amie space or a pokepuff of varying quality. You can wait to open the presents too, at least one row full of presents will stock up and you can open them at your convenience.

You don't need to be online to gather goodies either, but you have to at least have some friends stored in the PSS, so you have to have been online and "met" some people to kickstart this feature.