Yes, a 00 buckshot load will penetrate seven sheets of dry wall. That means it goes through three walls, loosing energy all the way, and lodges in the fourth.
5.56 mil on the other hand penetrated 12 sheets, six walls, and kept on going. I'd call that meaningful, as in at least 100% more penetration with 5.56 mil versus 00 buck. (In the same test 5.56mm also penetrated twelve 3/4 inch pine boards. Doubt I could do that with 00 buck.)
That translates into about twice the chance to kill someone you can't see and don't want to hurt downrange.
For apartment and condo dwellers there is an added factor. My apartment, like many others, is separated from the neighbors by a fire rated wall consisting of two sheets of dry wall and two sheets of 3/4th inch plywood, plus insulation. In my case most of the walls are also armored with about six inches of books. I am reasonably confident; confident enough to risk going to jail or facing a civil lawsuit that would break me if I ever have to shoot and I'm wrong, that this barrier will slow down a 00 load enough to prevent injury to the neighbors. I'm not so sure about a 5.56mm round.
There is also the fact that I can't legally own any rifle with more than a 10 round, internal, non detachable magazine. Where I, and about 36 million other people live, a shotgun is my best choice for home defense. I really have though this through.