Actually neither is true... the market for brown eggs is insatiable (no pun intended) since many Americans (and others) believe (erroneously) that they are somehow healthier. They bring a premium price as well.
Brown eggs can be certified Kosher, however, no egg, white or brown, can be consumed by Observant Jews, if it has any blood spots or brown spots on the inside. Sometimes, depending on the chicken variety, brown eggs can have small brown spots or blemishes on the inside, which renders them non-Kosher. This is one of the reasons that only non-fertilized eggs are considered Kosher. Brown eggs (Betizah) are part of a traditional Seder plate at Passover...