Nothing, there is no difference between Shiny Pokemon and normal Pokemon besides their colouring. People simply seem to crave having a Pokemon with a different colouration. They're really just there for the novelty and maybe to encourage trading.
This is, however, assuming that everyone loves Shinies which is false. I personally don't care about Shinies very much; all I see when I see a person with a Shiny is arrogance. Someone who likes to say "I've got a Shiny Palkia and it makes me better than you!", which is something I absolutely despise in people.
Also, as of X and Y, the Shiny encounter rate is doubled to 1/4096.