Eggs are an exceptionally nutritious food, as are all foods destined to nourish a growing animal. However, one concern lies in eggs' high concentration of arachidonic acid (AA), a long-chain omega-6 fat that is the precursor to many eicosanoids. Omega-6 derived eicosanoids are essential molecules that are involved in healing, development and defense. Some of them are inflammatory mediators that can contribute to disease when present in excess. Eggs are one of the main sources of AA in the modern diet.
The percent long-chain omega-6 fats (including AA) in red blood cell membranes associates quite well with heart attack risk. You can see the relationship in this graph compiled by Dr. Bill Lands. However, egg consumption has never been convincingly linked to heart attack risk or any other disorder I'm aware of, despite dire warnings about eggs' cholesterol content. Nevertheless, conventionally raised eggs are unnaturally rich in AA, and unnaturally low in omega-3, due to the hens' diet of grains and soybeans.
The ideal egg is one that comes from a hen raised outdoors (often on pasture), in a place where she can eat a variety of green plants and insects. Hens raised this way typically still eat grain-based feed, but supplemented with a significant amount of foraged food. This dramatically increases the nutritional value of the eggs, as I've noted before. Modern hens lay nearly one egg a day, which is a rate of production that can not be sustained without a large amount of calorie-dense food. They can't eat enough to lay at this rate by foraging.
Not everyone has access to pastured eggs. "Omega-3 eggs" come from hens fed an omega-3 enriched diet*. Not only do they have a much higher omega-3 content than conventional eggs, they also contain less AA. One study found that omega-3 eggs contain 39% less AA than conventional and organic eggs. Omega-3 eggs were also rich in short- and long-chain omega-3 fats. Omega-3 eggs are certainly not nutritionally equivalent to pastured eggs, but they're a step in the right direction.
I don't really know if the AA content of eggs is a concern. Eicosanoid biology is complex and it doesn't like to fit into simple models. I'll look forward to seeing more research on the matter. In the meantime, I'll be eating pastured eggs, and when they're not available I'll eat omega-3 eggs.
*Typically from flax seeds, but some operations also use seaweed. The hens in the paper I cited were fed flax. The hens managed to convert a substantial portion of the alpha-linolenic acid into the important animal fat DHA, and presumably EPA although it was not measured.