We are talking decoyed birds here. We live in a major crow flyway, on a hill above a pecan orchard. To say that I have shot a few crows would be a major understatement.
A crow's body is not that much bigger than a pigeon, and 8's kill pigeons quite well out to 50 yds. or so. (ask me how I know) No. 6 shot is just fine on crows, and will increase downrange energy significantly, but payload size, or choke constriction has to be increased to maintain pattern density.
btw, when you live in the country, and can shoot in your backyard, it's easy to experiment with guns/loads. One day a friend and I were doing some looong range experiments on crows. My friend was ranging the flock with a range finder, and I was shooting at them with an Ithaca Mag 10, with 2 ounces of #7 shot.
Conclusion: 10 ga. mags kick too much for me!
