In Pokémon X and Y, you get the Oval Charm () after completing the Kalos Pokédex, which increases your chances of getting an Egg at the Day Care. You get the Shiny Charm () after completing the National Pokédex, which increases the chance of finding Shiny Pokémon in the wild.
You also get a Diploma for completing each of the Pokédexes:
Central Kalos Pokédex:
Coastal Kalos Pokédex:
Mountain Kalos Pokédex:
Also your trainer card turns silver after completing the three Kalos Pokédexes.
Hope I helped :)