OK BACK TO BASICS>
a cylinder bore shotgun on average, will spread 1 inch per yard, after about the the third yard.
A full choke shot gun, will spread about 1 inch per yard, after about the 10 yard.
We are talking about using a weapon for defense INSIDE your home, after a break in. We are not talking about assaulting a barricaded crack house, breaking motor blocks at road blocks or stopping a PRC assault on a hill in Korea. WE are talking about defending your and yours against a common burglar/crackhead/banger coming into your home with bad intents.
NOW lets look at houses, a smaller starter home is going to run about 800 square foot, a big house is about 1500 square foot on the foundation. A really nice house is going to run 2000 square foot on the foundation. Thats 40 feet by 50 feet. Now doing the math we find out the diagonal on that house is 64 feet. thats corner to corner, the longest shot possible is 20 yards. Now that makes the assumption there are no internal walls, no furniture in the way, nothing, just a big open box. Which we know is not the way homes are built, but even if this were so, that means that a average shotgun, bored cylinder, is going to deliver a 17 inch spread. (20 yards, from muzzle to far corner, is the 3 + {17 x 1}. ) thats like getting hit with 27 .22 stingers all at the same time.
Now drop that down to a more reasonable distance, like say, the top of the steps to the bottom of the steps, lets say 4 yards if you have a "grand Staircase" thats like getting 27 hits to the chest with a .22 in a 1 1/2 to 2 inch circle. Do that once or twice more, and you have what"s called hamburger.
Now not making light of all sorts of gelatin testing and what have you, I have seen the results of a 12 gauge blast at close range with just #6 six shot, and i have been shot with 6 shot at fairly long distance, and a few #6 shot penetrated across my back several inches, and that was at well over 30 yards, and maybe closer to 45. The hunting accident I helped recover a body on was a hunter shot with 6 shot at about 3 yards, as far as we could tell, and there was a hole thru the victim, the entrance appeared to be golf ball sized, and the exit was much larger. Clearly at that range penetration was complete on a human body.
Now for the do it yourself tests. get a tshirt, pack it with wet newspaper, and stack it on a log, where you have a safe back ground. Now using a tape measure, measure inside your house what might be the longest practical shot you are going to have in a home invasion. At the test sight, measure that out, then aim and shoot that wet newsprint, and see what you get.
I think you will find that you answer is self evident.
So unless you live in Buckingham Palace or are a crown prince in Saudi Arabia where you use a golf car to get around your home, a twelve gauge with 4 buck is going to be darn near perfect.
One other point rarely thought about, is miss's. If you miss with a slug or 000 buck, that miss is going to travel on a good distance, and you MIGHT at the time of need, think about that, and say to yourself, I need to wait a second to shoot or I will hit "bill and alice" next door. Shooting 4 buck, after 60 yards of so, its not going to be as lethal as a slug or 000 buck. so don't worry, shoot when the shot is there, rather than worrying.