Other than there apperance.
>Shiny Pokemon is VERY EXTREMELY RARE! you have a chance 1/8192 to catch shiny pokemon! in a lifetime, I just saw a shiny pokemon once, a Shiny Rattata only. so, if you have one, you're so lucky and may proud to yourself[-Whats so special about shint pokemon?]
You could hack, though. Your comment question answer: No there is no change in stats except in Gen 1 you have 31 IVs in each stat if you see a shiny