Although brown eggs are considered to be more nutritional than white eggs by most of the people, there is no difference exists between the two whatsoever.
The only difference other than their colour is the type of chicken it comes out of. Various breed of hens lay different colours. Hens with red or brown feathers and matching-coloured earlobes lay brown eggs whereas white feathers and white earlobes give white eggs.
White eggs are preferred by consumers since it looks clean and fresher than brown eggs. Some people prefer brown eggs because it is easier to differentiate the shell when it falls into the food that is being prepared.
Summary:
There is no nutritional difference between white and brown eggs
The colour differences believed to exist because of the type of hens that lay the eggs.