The standard egg that you will find in the grocery store is white in color and most likely came from the Leghorn breed. Like Foghorn Leghorn, but he will never lay an egg, because he's a rooster. Only hens lay eggs.
I happen to have four chickens in my backyard. They all lay brown eggs; that's because they are heritage breeds. You will not see a single heritage breed on a factory farm, but you will find them on organic farms. Hence, the brown eggs in the organic isle.
What makes my chickens' eggs better than store bought is that I feed them quality food, and they get to roam free to dig up bugs and worms. They also get to eat grass and dandelions, and other weeds that chickens eat. Because of my good care taking for them, they are happy, stress free chickens. They produce eggs that are lower in cholesterol and have a higher nutrient value. And the yokes are the most creamiest that I've ever had.