Brown eggs are the healthier, more natural, more wholesome choice, which is why they often cost more and why the farmers' market crowd reaches for them. White eggs feel like the cheap, mass-produced option. Brown just looks more farm-fresh.
The colour of an eggshell tells you the breed of the hen, and nothing about the egg's nutrition. As a rough rule, hens with white feathers and white earlobes lay white eggs, and hens with reddish-brown feathers and red earlobes lay brown ones; that is the whole story. Inside the shell, brown and white eggs are nutritionally the same, with the same protein, fat, and vitamins, all of which depend on the hen's diet and living conditions, not the shell pigment. Brown eggs often cost more simply because the breeds that lay them tend to be bigger birds that eat more feed, so they are pricier to produce, not because the egg is superior. A hen's diet and welfare genuinely affect quality, but you cannot read any of that off the shell colour. So the wholesome brown egg and the humble white egg are the same breakfast in different wrapping. You are paying extra for the hen's plumage.