my take, to be redundant.
i'll just use buckshot as the example. i believe 00 buck is .335" diameter, 50-60 grain - so basically about the same diameter as a 9mm bullet, just lighter. now you figure you have 10-20 of these flying out between 1000 and 1400 fps, both depending on whether you're shooting normal or magnum shells. so on the high end, comparable to 9mm velocity and diameter, just less mass per. let's say ideally half of them hit at the range you'd be using a home defense shotgun. that's a lot of damage and energy, and i've read that multiple traumatic wounds incurred simultaneously create shock faster than several hitting in succession over a time period. same could go for birdshot, although the penetration wouldn't be what it needs to be to assure high single-shot stop ratios, not that those are the be all and end all. slugs will mess anything up, when the box-of-truth guys did their bulletproof glass test i definitely started giving a lot more credibility to shotgun slugs.
at close range nothing's better than a shotgun. whether or not it's flexible or the best choice in very close quarters is arguable, but in terms of the old "stopping power" premise, you're not going to find much better.