Absolutely Nothing
The only thing that changes when a Pokemon is shiny is it's coloration. They do nothing to the stats, nothing to the ev's and nothing to the iv's.
The only reason that shinies are wanted by people is that they are rare. In x/y you have a 1/4096, before x/y you had a 1/8192 chance. They are valuable trading tools and sometimes people like them to show how much they work in Pokemon.
Having shinies can also make people very arrogant. Some people think that if they have more shinies than you they are better at Pokemon than you. My opinion on shinies is neutral. I only use them for trade tools. Hope this helped!