Eggs come in a variety of colors -- white, brown, blue, green, and speckled. The difference in shell pigmentation is superficial, but the reasons are genetic and evolutionary, dating all the way back to dinosaurs.
Let's start with the familiar white and brown chicken eggs. You might have a preference, but one doesn't have more protein or a better taste than the other, though brown eggs tend to have slightly more Omega-3 fatty acids.
Brown eggs also come from larger chickens that cost more to maintain, which is why those eggs are a little more expensive. It's not because they're way better. Brown eggs get their color from a biochemical pigment called protoporphyrin formed by blood cells breaking down. And of course biochemical pigments are due to genetics.
White-feathered chickens with white earlobes called Leghorn chickens lay white eggs while one type of red or brown chickens with red earlobes called Orpingtons lay brown eggs. But, it gets weirder. The Americana breed lays blue eggs, giving it the nickname of the Easter egg chicken. Olive Eggers, a cross between a hen and rooster that are from a brown egg and a blue egg laying breed, lays olive green eggs.