"A rose by any other name would smell as sweet" and a white-shelled egg by any other color would still have the same inside make-up!
It's true! The only physical difference concerning eggs is in the color of the shell. Yes, there are people who say brown eggs taste better, and that probably is true in many instances, but the taste difference comes from the diet of the hen, not the color of the shell.
White-shelled eggs you buy in grocery stores come almost exclusively from caged layers that eat only a total ration concentrate, and the eggs they produce have pale yellow yolks along with their signature taste.
Brown eggs usually come from floor or range birds that usually are fed some whole or cracked grain along with their laying feed, and many have access to outdoor feeds such as plants, worms and bugs. This diet yields eggs with a darker yellow-orange yolk and a different taste than the white-shelled "store" eggs.
Bottom-line: if you have a mixed flock of white and brown egg layers fed the same and raised with each other under the same conditions the eggs will taste the same!
What causes shell color? Colored egg shells are the result of pigments added during shell formation.
Brown-egg layers produce eggs of varying shades ranging from barely tinted to nearly black. The darkest shells come from Barnavelders, Marans, Penedesencas, and Welsumers. Most of the pigment of a brown egg is deposited in the bloom, the last layer added to the outside of an egg just before it is laid. The inside of the egg shell is pale or nearly white. Bloom dissolves when wet and easily rubs off when dry. This is why cleaning a brown-shelled egg removes some of the color.
The pigment of a blue-shell egg is spread throughout the shell, making it just as blue on the inside as the outside.
Green shell eggs come from crossing a blue egg layer with a brown egg layer, resulting in blue shell eggs with a brown coating which gives the egg a greenish color.
The many different shades laid by "Easter Egg" chickens (Ameraucanas) results from blue shell eggs coated with different shades of brown bloom.
One final note about shell color: as a general rule, hens with white earlobes lay white-shelled eggs and hens with red earlobes lay brown-shelled eggs. And, of course, to prove the rule there are exceptions. Crevecoeurs, Dorkings, Redcaps and Sumatras have red earlobes but lay white-shell eggs; Araucanas and Ameraucanas have red earlobes but lay blue shell eggs; and Penedesencas with white earlobes lay eggs with the darkest brown shell of all!
Finally, remember that no matter the color of the shell all chicken eggs produced under the same conditions will taste the same!