Dave, because I am primarily a bird hunter I use my shotgun for 80-90% of all the hunting I do.
For HD, in my opinion familiarity and comfort level with a gun is very important. I've shot so many thousands of rounds through my 870's that even picking it up in the dark, I could check to see if it was loaded, and if it wasn't, LOAD it, pretty much by instinct very quickly.
I also regularly pattern and shoot heavy 3 1/2 inch goose loads, 3 inch magnum duck loads, turkey loads, etc. So at least for me, 3 inches of hevi-shot T's is just another shotgun round and recoil in my 870's doesn't really enter into the picture. (is it possible to shoot a particular gun so muich and be so familiar with it that you almost become........"recoil proof?" That's how I feel with my 870!!!!)
I am NOT a good shot with my handgun. Chalk it up to a SEVERE lack of practice! I'd have better luck staying on target with quicker follow up with just about ANYTHING out of my 870 (hevi-shot included) compared to my Ruger 9MM.
Can't argue with the energy, weight, size, and speed of the dead-coyote pellets, either.
But as you point out, a shotgun blast at close range with damn near anything loaded up is likely to be terminal. It's almost like the 9 MM vs 40 cal arguments (energy vs recoil vs etc,etc,etc). It sound slike we both agree that controling point of aim and adrenaline and falling back on experience, repitition and training are perhgaps more important than what's loaded up in the gun.
I still love my 50 20 cal pellets though!