I live in Canada so I can't compare directly to a USDA Organic chicken. However, based on a chicken one could get from Whole Foods, for example, our bird has a much richer flavour and a firmer, less rubbery texture. This part is very subjective, of course, but in a side-by-side comparison you would definitely be able to taste and feel the difference.
We also raise our birds to be much heavier than a store bought bird - on average about six pounds after processing vs three-ish pounds in the store. I'd wager that your meat-to-carcase ratio is probably higher for one of our birds, giving a better value. (Actually, it's better value regardless - we sell our birds for $4/lb vs $5/lb for the broiler barn organic birds in the store.)
Environmentally, there's less concentration of pollutants. All of the chicken manure goes straight on the grass and is a primo source of nutrients for subsequent hay crops. For me it's a win - I don't have to apply fertilizer nor clean out chicken barns.
Coming from an animal welfare standpoint, just because you're buying "organic" chicken in the store, doesn't mean they've been raised in a humane fashion. I carry no guilt in eating our chickens. They're not overcrowded, debeaked or in a dusty, foul smelling environment. They live as well as I can provide up until the day they go for slaughter.