dead on. The stop power is really what you're looking for. For HD, you have the luxury of knowing your home. Plan out your shots ahead of time. Where can you fire a heavy load and not hit someone on the other side. My scattergun is loaded w/ 00 buck at home. I don't wanna risk not stopping someone. Plus, in my state, I'll go to prison if the bad guy isn't "threatening" me, thus, its my word against a dead guy with heavy load. With a smaller load, he might be around to testify.
As for hunting, I'd say the recommendations above are pretty dead on.