If the chickens are just fed feed from the feed store and can't get out and find their own food the eggs are going to taste the same as store bought eggs.
Were the difference comes in is if the chickens have a natural diet of grass, bugs, and any small animal they can catch and kill... then you get dark orange, thick, richly flavored yolks. Other wise the only thing you are gaining by raising your own chickens for eggs is that you know what your chickens are eating (you know they aren't being fed hormones or antibiotics which you will get trace amounts coming out in the eggs you eat) and you know they are being cared for in a much more humane way.