A quick wander through some tables suggests that common .410 slug loads versus common .357 magnum loads are surprisingly similar in muzzle energy when fired through the same length of barrel. However. The .410 is fatter, which means a bigger wound and faster energy transfer. The .357 magnum is known to send bullets in one side and out the other of medium sized game, so it has more velocity than it can really use: all else being very approximately equal, you want the biggest possible hole provided you can get at least halfway through the target.

The .357 mag very quickly dominates as the range opens up, but in your typical self defense situation 5 yards is long range. So retained energy is a moot point here.

My opinion is that .410 slugs would do a pretty good job on a human at short ranges. Not any better than other alternatives, though. When you consider how expensive .410 slugs are to practice with, and how limited the selection is next to the wealth of good quality hollow points in handgun calibers... Probably not worth the effort. If you're going to use the .410 for self defense, you probably want it full of number 4 or 5 pellets on the theory that a hundred hits is better than one. That's a hundred chances to get lucky with an eye or an artery, plus it's going to cause absolutely horrific flesh damage. The sheer pain would disable any non-drugged attacker. The only limitation here is abysmal range, but again, in self defense range is hardly ever a problem.

I'm with Horn Dog on the .44 magnum: The .410 slug and .357 mag are dealing with numbers in the 500-700ft# area for muzzle energy, while the .44 magnum can easily develop over 1000ft# from a handgun, 1200ft# if you shoot it in a carbine. Totally different animal.