Egg shell color is determined by the breed of hen and is often related to the color of the hen’s ear lobes. White eggs are most often laid by white or light-colored hens with white ear lobes, while brown eggs are most often laid by red-feathered or brown/dark-feathered chickens with red ear lobes. The color of brown eggs is a natural pigment placed by the hen on the surface of the shell during the final stages of egg formation. The outer shell color can vary from light to dark brown, depending on the breed of the hen and on individual hen characteristics.
A brown egg or a white egg will give you basically the same nutrition, taste the same, and are equally delicious. The two also have more or less the same shell thickness. The differences in shell thickness that may be observed likely has to do with the age of the chicken — young hens lay eggs with shells that are typically harder than older hens’ eggs, but this is true for both white and brown egg layers.