I think collecting large amounts of food scraps from such sources is fairly rare, but feeding food scraps from the household seems pretty common.
I don't know about chickens vs. ducks.
But as regards chickens: if someone gets just barely enough scraps, so the chickens eat every bit, they will probably not get a balanced diet. But if you let the chickens pick through a large amount of food scraps, they will do better, because they eat the parts they want and skip the things they already have too much of. It probably does not make a perfect diet in any case, but it might be good enough for hens to lay eggs for a while, or males to grow big enough to butcher.
Of course it will depend a lot on the scraps-- doughnuts are different than scrambled eggs or salads! A mixture of foods would give the chickens the best chance of picking a suitable combination to eat.
A number of people provide a complete, purchased feed and ALSO offer food scraps. They generally say the chickens eat some feed and some scraps, and seem healthy and productive.
The easiest way to provide a balanced diet for chickens is to purchase a complete feed for them. But many other ways do work, depending on how much effort the person is willing to put into it.