Many, many moons ago when I was young and living with my parents, my DM kept hens and sold the eggs to the egg packing station who collected them weekly, scanned them for blood spots, etc, and stamped the little lion on them. We had about 300. Two sorts raised from chicks which she bought as day olds to be raised in an incubator at the end of the hall (we never used the front door anyway). They were a commercial breed - Thornbers 404 (not sure of the spelling) which were brown, chunkier birds and laid brown eggs and Thornbers 505 which were white, smaller, flightier and laid white eggs. Kept in runs and fed the same. Apart from the egg shell colour the egg inside was exactly the same. There is no difference. Back then no one particularly cared about egg shell colour, more about the hens and how they were fed. Then the media decided that brown eggs were better and we stopped keeping white hens as no one wanted the eggs.