You can have one or the other, but not both, not in abundance. That seems to be the lesson I learned in the past, of which I've been reminded by a couple of the organic/gardening blogs I visit. We had a "slop" pail, into which went the vegetable scraps, beet tops, sour milk, etc. After lunch we'd top the pail up with some water and use it to wet down the chicken mash still left in the feeders. The hens would be attracted, both by the wet mash and by the slop, eat a bit more and presumably lay a few more eggs. And also excrete more manure, which dad and I would have to shovel from the house into the manure spreader to spread on the field. (Hen manure is much hotter than cow manure, so it had to be spread much thinner.)
My mother maintained a compost pile outside, under the lilac bush or in her garden, but with the competition from the hens it didn't really accumulate much. (Enough for her to brag about it though--compost in 1950 was just a tad rare in upstate NY.)
As I mentioned, a couple of the sites I visited mentioned the same sort of competition--you can feed vegetable scraps to the pigs, which are omnivores like us, or you can compost, but not both in full measure. (You also need a balance of materials for the compost, which is hard to achieve in ideal measure over the course of the year.) These are some of the little complications of organic gardening.