Free ranging with plenty of grass and quality supplimental feeds make far better eggs. That's what our customers say. 'Best eggs ever tasted' often said and demand outstrips supply three-fold. But a lot also has to do with the breed and the size of egg. The slower egg producers seem to taste better. Our Leghorn bantam's eggs are fantastic and not for sale. We bought some supermarket free range eggs a while back -tasted of nothing, just looked right. Most of our eggs are medium sized from Wyandottes, some from Orpingtons. Only one hybrid left and we won't get any more -lays loads of big eggs but they don't taste as good. Eats disproportionately more pellets as well. Best feed to egg production ratio by miles are the leghorn bantams.
Meat taste seems to be about growth rate, so breed rather than feed, but I'm sure free ranging must add something. Like lamb -Jacobs taste far better than Texels in our experience.