White and brown eggs are nutritionally identical, and, on the inside, they are physically identical as well. Despite what you may have heard about how one is more natural or nutritious than the other, both white and brown eggs are products of real, live chickens, and their exterior color is not an indicator of nutritional content or anything else, beyond the breed of chicken involved in egg production.
Shell colour is generally not as a result of diet it is generally believed to be genetic and even more specifically certain breeds of chicken

lay white eggs and other breeds lay brown eggs.
A rough guide is that white eggs are produced by hens with white feathers and earlobes whilst brown eggs are produced by hens with red feathers and red earlobes.

Just like the nutritional value, there is no difference between brown and white eggs in terms of flavor. Some people are of the opinion that brown eggs are tastier than white ones, but you will probably not notice that ‘slight’ difference.

What’s more, some commercial egg producers try to fool people by providing “special” brown eggs at a much higher price.

Health Benefits

An egg is one of the most nutritious food items in our diet. It is rich in minerals, proteins, and vitamins, all of which are easily absorbed by the body

 Nourish expecting mothers and their babies: Egg yolks contain high levels of biotin, a B vitamin that can prevent birth defects. Egg yolks should be a baby's first animal food and can be introduced around six months.

Vitamin Content of Eggs: Eggs are rich in vitamin B, especially vitamin b12, vitamin A, vitamin D, vitamin E and vitamin K. It should be noted that very few food items that contain vitamin D, egg being one of them.

Protein Content of Eggs: An egg is composed of about 11% proteins. Further it contains all the amino acids necessary for body metabolism. This makes eggs an essential part of the diet of those who wish to increase weight and build muscles. Most of the proteins are concentrated in the white part of the egg, known as albumin (albumen) or egg white.

Egg White and Egg Yolk: There are two essential parts of an egg; the albumen or the white part and the yolk or the yellow part. The yolk is suspended in the albumin and contains about 80% of the calories and almost all fats present in the egg. It contains vitamin A, D, E and K and minerals such as iron, calcium, and phosphorus. The egg albumen mostly contains water and proteins.

Health Benefits of Eggs: The nutritional value of eggs makes it good for immunity, strong vision, treatment of macular degeneration, cataract treatment, skin care, nervous system, strong bones, and blood formation. Recent research has also shown that consuming eggs does not lead to increase in serum cholesterol levels.

Vitamin D: Eggs are one of the only foods that contain naturally occurring vitamin D.

Healthy Hair: Eggs promote healthy hair and nails because of their high sulphur content and wide array of vitamins and minerals. Many people find their hair growing faster after adding eggs to their diet, especially if they were previously deficient in foods containing sulphur or B12.

Keep your brain healthy. Choline is an important nutrient found in egg yolks as phosphatidycholine. . A cell must have this substance to be normal and healthy and to work properly. It keeps the membrane of each cell in a fluid condition.