The colour of an eggshell is determined by the breed of the hen, not by how nutritious the egg is. Brown and white eggs of the same size and diet are nutritionally almost identical.
What actually changes an egg’s nutrient profile is the hen’s feed and living conditions — for example, eggs from hens fed extra omega-3s can contain more of those fats.
The takeaway
Choose eggs based on freshness, price and welfare standards rather than shell colour. Brown is not a health upgrade.