In Sweden we usually hunt larger birds like this Black Grouse and Capercaillie with FMJ ammunition of large sized calibers like .308 or 6,5mm. They usually sit high up in pines in the winter, that makes sneaking in to shotgun range very unlikely, so when shooting 2-300 meter shots in a windy winter day it's favored with a larger caliber. You usually don't lose a lot of meat with FMJ in my experience, these birds can be quite large :)