Explanation
No. A brown shell does not give a chicken egg a nutritional advantage over a white shell. Shell color is not a nutritional rating.
The Illinois Department of Agriculture explains that shell color depends on the hen's breed and does not affect nutritional value. Michigan State University Extension independently explains that differences in shell color come from genetics and breeding, rather than differences in nutritional quality caused by the color itself.
Shell color and yolk color are also different characteristics. The hen's diet can influence yolk color, while genetics determines shell color. Neither a darker shell nor the contrast between shell colors establishes that one egg is more nutritious.
Key takeaway
Brown and white shells reflect differences between hens, not a nutritional ranking of their eggs.