That said, the colorful eggs from your backyard hens WILL have much more nutrition, because eggs produced by hens raised on pasture are much healthier, indeed (and they taste much better, too).
Keep in mind that commercially produced "free range" eggs may have been laid by hens who have never seen a blade of grass, the sun or the sky. "Pasture-raised" is something different, and much healthier. Eggs laid by hens raised on pasture have less fat and cholesterol, and more healthy vitamin A, vitamin E, beta carotene and omega-3s. You can read all about the nutritional differences between factory farmed eggs and real, eggs to get an idea of what all those people who have to eat those icky grocery store eggs are missing!