Generally back in your grandma's day the commercial hens were of Mediterranean descent, which lay white eggs. The breeds people had on small farms were brown egg layers.

I have hens who lay white, brown of all various shades, and blue/green shells. Inside they are all the same nutritionally.

The difference nutritionally comes from the hen's diet. If the girls are eating grass and bugs, their eggs will be nutritionally different than those who only eat commercial feed. This could be why people thought brown eggs were better for you. (For a long time I believed the misconception that egg shell was diet-related. Now that I have hens I know otherwise. )

I think of it like this: if a mother breast feeds her baby and eats a variety of fruits, vegetables, and protein sources, the milk will be of different quality than if she only ate cereal fortified with artificial vitamins. The quality of the milk at that point would be determined by how "bioavailable" the fake vitamins are.

Also, when you see "hens fed a vegetarian diet", it irritates me for a number of reasons. Chickens aren't vegetarians in the wild, and the commercial feed ingredients took a turn after the whole mad cow scare a while ago. Now the protein in the feed is almost always soy, unless you go out of your way to find non-soy feed.

I have seen my hens gobble down Japanese beetles and a freshly killed mouse my neighbor's cat caught and left on the ground. Vegetarians indeed.