I believe in greens as an important part of a bird's diet. Particularly fresh, young, tender greens that are alive. When my birds are in their breeding pens, they are brought some daily. My opinion is that if we do not bring the birds fresh greens that are confined, we are not doing as we should. Historically, poultry breeders felt the same. BUT, they did not have the complete rations that we do today. That was their vitamin, mineral supplement. So my position is an opinion, not a fact. It would not be true to say that someone was neglecting their birds because they did not. My opinion is in part based on the greens being alive. Their is a lot to be said for food that is alive.
I am a strong supporter of birds on range, in particular growing birds. I do not believe their can be a better substitute. I attribute this more than anything to access to a variety of herbs, grasses, and greens. I want them to have all three though I understand that coarse mature grasses should not be a large part of a bird's diet.
I say the above because it is impossible to overstate the importance of fresh air, sunshine, and tender greens.
On the other hand, our birds are not cows, sheep, rabbits, or horses. They are not high fiber animals. They are not ruminants. They are seed eaters. Sheep or cows do not require the amount of energy that our birds do. Our bird's heart rates are in excess of 250 beats per minute. They have very high respiration rates. They require a lot of energy to maintain this super high metabolism. They are more than anything, seed eaters. They need more energy (seeds) than any other thing.
Cows are not big seed eaters. They are great converters of high fiber, low protein grass into flesh. They have comparatively low metabolisms and are equipped to get the most out of little. They are not made to process high energy feeds (corn), like a chicken is. It used to put on fat, because people like marbled beef. Not because it is best for the cows.
Your poultry meat will be more nutritionally dense, because of the added time required to develop that flesh. Also that the birds get more exercise. The flesh will more developed. Any improvement in the eggs would be from the variety of feed stuffs that they have access to.
So I believe and emphasize the access to greens for our birds, but will hold to that grains and legumes should be the majority of their diet. They need more than anything (in qty) energy.
Ducks, and especially geese, are better converters of green forage.