Nothing.
Mmm... Breakfast.
White or brown color does not make an egg healthier, tastier, or better. In fact, even if you find blue or green eggs, they'll be the same too.
The chicken on the left is a Rhode Island Red and lays a brown egg. The chicken on the right is a Leghorn and lays a white egg.
The color of the egg depends on the breed of the hen. Leghorns, Dorkings, Minorcas, and Andalusians lay white eggs. Brahmas, Plymouth Rocks, Wyandottes, and Rhode Island Reds lay brown eggs. Araucanas and Ameraucanas lay blue or blue-green eggs.