All of these important health benefits are derived, in part, from the condition in which the hen was raised. The diet that the mother hen has will obviously be reflected in the nutrient content of the egg. For that reason, it is a far better choice to consume pasture-fed eggs, as they have consistently been shown to have higher omega-3 content, vitamin E content, tend to be larger, and are more densely packed with nutrients.
While the price tag might be slightly higher for organic, free-range, or cage-free eggs, if you are serious about getting the most health benefits out of eggs that you can, dig a bit deeper in your pockets for those extra coins.