Officially, there is no difference between white and brown eggs, or between organic and conventional ones. However, many people claim to prefer the taste of brown eggs and I know several people who get a stomachache from eating too many conventional ones.
That said, freshness and feed do make significant differences and are difficult to track. These may be the factors that are really in play when people find differences between types of eggs. Free-range and pastured hens definitely have better diets and produce better eggs.
One way to test an egg for freshness by floating it in cold water. Fresh eggs will float on their sides while older eggs will "stand on end" in the water. Even better, crack open the egg and check the white. An old egg, while still safe to eat and legally "fresh," will have a watery yolk that runs all over the pan; it takes a truly fresh egg to make the classic round, thick-edged fried egg.
To freeze eggs, break them into a container. Pierce the yolks with a fork and gently mix the whites and yolks, creating as little foam as possible -- foam will dry out the eggs. Whites frozen by themselves do just fine, but separated yolks will do best if you add a bit of salt to those intended for cooking and a bit of sugar to those that will go into baked goods.
Note: a "no antibiotics" label on a package of chicken meat is of dubious value. Years ago, they experimented with antibiotics as a way to increase the weight of chickens, but found that it was not cost-effective -- the drugs cost more than the additional weight could earn. Now, chickens seldom get antibiotics unless they need them.
