Kenji López-Alt from Serious Eats made a randomized, single-blind and kind of placebo-controlled study with six kinds of eggs:
- Plain old factory farmed eggs
- Eggs with 325 mg Omega-3 Fatty Acid per egg (not organic or cage free)
- Organic Cage Free eggs with 200 mg Omega-3 Fatty Acid per egg
- Cage Free eggs with 100 mg Omega-3 Fatty Acid per egg
- Organic eggs, no other specifications
- Organic eggs from free-roaming, pasture-raised chickens
His verdict after making scrambled eggs in a controlled environment: It doesn't matter. Instead the actual contents of the eggs the color determines the perceived taste.
Concerning frying the eggs sunny side-up of poaching: Freshness matters. The fresher the egg, the tighter the egg white and yolk. If the egg is older, the yolk and the egg white will lose liquid which is the looser albumen part of the raw egg. This causes the egg to spread while frying, making tegg less appetizing than an egg with taller standing yolk. When poaching, the looser egg white causes the ugly white flakes (https://youtu.be/66btvAWmp7g?t=1m25s (1:25 min to 1:48 min)).
I guess, if you get eggs from free-roaming chickens the eggs might be just fresher than the factory farmed eggs and this is why eggs from free-roaming chicken might tastes better and are easier to process in some cases. (Not, if you plan to boil those.)