If you have to decide between a carton of brown eggs and a carton of white, don't even bother considering the eggs' colours. Just look at the price tag, because the eggs are essentially the same.
It might seem like brown eggs are healthier for you, since they tend to cost more than their white counterparts (and things that cost more are usually better, right?). However, Cooking Light points out, if you choose brown eggs over white and pay a 25 per cent price premium, it's basically an aesthetic choice.
Brown eggs and white eggs have the same proportion of yolks and whites and the same nutrients. Brown eggs just tend to come from bigger chickens that require more feed, and so farms price them higher to make up for the added cost.
Today I Found out has more details on the white vs brown egg debate, but the short of it is brown eggs and white eggs are the same on the inside, where it counts.
Nutrition Mistakes [Cooking Light]