RE: #6 SHOT
With lead shot, you can take birds out to 40 and 45 yards. Much beyond that depends a lot on the speed of the load you have chosen to hunt with. If you have a load that is 1150 at the muzzle and are shooting plain old lead, it starts to get iffy past 45. On the other hand, loads leaving the barrel at 1300 will certainly do the job everytime in the right gun and through the right choke. (EDIT: BTW, the ranges I am giving here are speculative, and based just on speed/energy data and related experiences with other hunters and industry leaders... I've been blessed to have never crippled a bird...touch wood).
If you are shooting high density/hevi-shot, then shooting a #6 is just like shooting a #4 (so the numbers say). But no matter how you slice it, you're getting more energy out of that heavier pellet. I took my first Rio with #6 Extended Rage at 56 yards, measured by rangefinder, and that bird acted like he'd been hit by a line drive off David Ortiz' bat. A bit of a wing flap and waggle and that was it. Never so much as kicked his legs or flapped his wings or flipped over. Just down and out.