What really bugs me about these discussions is everyone seems to think in TWO dimensions.
Think of stopping power as THREE dimensions, with the most important being the length of the penetration channel. In other words:
a 30-06 works VERY well with a light bullet because the wound channel looks like this:
Pictures from Martin Fackler:
a 125 grain .357 wound channel looks like this:
and a .45 ACP like this:
And a 12 Gauge like this:
If the shotgun is a magic wand, one might look at projectile weight as the magic in the formula.
over 540 grains of lead has a serious effect on targets, in most any form.
Perhaps if one wants shotgun like stopping power, one should start looking at handgun calibers that more then double the bullet weight of either the .45 ACP, or .357.
IIRC: .500 Linebaugh max 525 grains, 1350 fps, 525 grain .510 bullet for max, a .500 JRH that did in an asian buffalo, a Hawk 325 grain thin jacketed .510 bullet for deer/BG's, .475 Linebaugh Hornady factory 400 grain XTP @ 1350 fps from my gun, 325 grain flat point going 1500 fps with low recoil, low pressure loads, in .475,
300 grain HP Hawk @ 1560 fps with low pressure loads, 45 Colt, 45 ACP/Super, and .357 mag.
.475 Linebaugh FA 83 loaded with 400 grain Hornady XTP, at 1350 fps. Heavy, expanding, and fast is best.
Makes a great pillow.
Res ipsa loquitur.