When you quit picking up fried chicken at Colonel Sanders place and started pursuing your Galliforme fare with bird dogs and shotgun you left the rational world behind.
But if you are determined to choose the most rational gun for use in an irrational pursuit probably the most effective gun on a covey of bob whites covied under a mesquite tree would be the Ithaca 10 gauge automatic that shoots 3-1/2" shells. Perhaps handloaded with 3 ounces of number eights. I bet with a five shot burst you could ground swat the whole covey. The weight wouldn't matter if you were leaning out the pickup window as you wouldn't have had to carry it anyway.
But I enjoy hunting behind a couple of my Brittanys, perhaps with a 5lb-5oz 28 gauge Parker Reproduction, double triggers, straight grip splinter forend. The shells are so small I can put an entire box in one pants pocket, 3/4 oz. of #8s. The dogs are on point. I walk in and flush the covey and manage to down a bird. One of the Brittanys retrieves it to hand. Much prettier picture and more satisfying experience I believe.
Hunting with a twelve is somewhere in between I think.
