We have had chickens in the past, and while I fully support anyone wanting to do their own chickens, the level of effort to keep them clean and healthy, safe from predators, and the labor to take care of them is non-trivial. They were the most expensive and labor-intensive "free eggs" we ever had.
It is a lot of work, but after my last group was killed off 2 months I have not impressed by store eggs, so I'm planning on re-enforcing my coop so I can get another group of them soon.
Curious to know what differences do you discern between store and fresh eggs? Not doubting you, just curious to know.
Note the wide variety. When you're doing a backyard chicken coop, you can pick whatever you want, for whatever reason (Rhode Island Red for hardiness, say, or a combo for variety). So not only do you have feed variation, you have breed variation, which can contribute to taste differences.
You also have freshness, as you use the eggs within a day or so of laying.