"Research shows that eggs from pasture-fed hens have more folic acid, vitamin B12, vitamin E and carotenes than hens fed only grain or pellets. US research confirms that there may be a nutritional difference between free range and other eggs. However, some researchers have claimed that free range and cage laid eggs have the same nutritional value.
Some studies were undertaken specifically to demonstrate no difference. The research was funded by the corporate egg industry and the hens used were all beak trimmed. The 'free range' hens used in the research may have been allowed access to the outdoors, but as their beaks were trimmed, they could only eat the same grains and food which were available to birds in cages.
Any beaked trimmed birds have great difficulty eating grass, or picking up worms, spiders etc without a full beak - that's the fundamental problem with running large flocks of birds and calling them 'free range'. There are similar problems with much of the 'research' conducted here in Australia. The researchers often mean well, but the funding is provided with strings attached and linked to specific outcomes - so they are often required to meet those specified objectives rather than paint a true picture as a result of their findings."
http://www.freeranger.com.au/
I can't remeber where I read it originally but this pretty much sums up what I remember. And from memory it is the carotenes that make the yolks yellower and the chickens (and us) get these predominantly from green leafy veges
Looks like there is a difference of opinion on that:
http://www.foodandnutrition.org/May-2013/Why-Are-Some-Egg-Yolks-and-Eggshells-Different-Colors/
I would prefer chickens fed a diet of pastured grasses. But again, show me the science
