I live in Colorado, but I would vote for Alaska. I'm trying to move up there and I love hunting here. I have access to private lands for Mule Deer and Pronghorn. Colorado has the largest herd of Elk in the US around the Meeker area and I was able to get two tags this year and most of the mountains are still public access.
All that said we don't have the variety of big game that Alaska does, plus the fishing is out of this world from what I here. I'm not into the birds so I don't know what the bird hunting is like but I bet it is pretty good. I think overall that Alaska is a sportsman's paradise.