We bought property, inherited chickens and one obnoxious rooster.
There is a difference! Please understand I am entering this from a freshness aspect. The white store bought eggs have a runner white. The yolk is not vibrant yellow orange in color. They are lighter in weight and volume. Eggs run watery when cracked. The taste factor is low. Like tofu, white eggs pick up flavor from others.
Fresh brown eggs have a richer density, they feel heavier when cooking. More substance when chewing them. There is a hint of sweetness. Hens fed a high protein feed and fresh clean water produced more quality eggs. Our hens where allowed freedom during the day and are lots of bugs and slugs. (In Oregon, there are ALOT of slugs). Lots of sunshine or rain depending on time of year.
We had ducks and geese, now we are talking really great eggs! But that is for another time.
I have bought brown eggs from the supermarket and whole foods/natures type stores.
In my humble opinion, they are no better then white eggs.
Personally I think, by the time they are packaged and sent to market, then sit waiting to be bought, they loose freshness and vitality.
The expense to have hens and do it properly outweighed the cost of having hens and cleaning their coop.