I've killed more than few deer with buckshot. For me, I always used Number 1 buck. It patterned well out of my mod choke Mossberg 500, and always seemed to me to be the best balance of shot size vs shot count. Always 3" mag loads too, except one time I shot a deer with a short magnum load. He didn't seem to notice the difference. My longest shot was about 45-50 steps my closest was about bayonet range. No 1 did the job.
Having said that, I will admit that I was impressed with 000 buck which had only been around, at least as far as I knew, a few years when I stopped hunting. That stuff killed like lightening. Those big pellets snap bones like toothpicks.
My only experience with 000 was a miss. A big doe came by me (we hunted with dogs) and I drew down on her at about ten yards. When the gun cracked she shifted gears and went out of there. I stood there like an idiot, completely forgetting I had two more shots in the Remington 1100. I MISSED HER?!?! WHAT THE........
I walked over, and there in the side of a little tree, about six inches in diameter was the the entire pattern of 000 buckshot. All twelve pellets. You could have covered them with a coffee cup.
I lost my shirttail that day.