The answer is in the concept of explanatory variance. Expert opinion (or whatever) would indicate that there is little difference between a quality 9mm round or 45 ACP. Thus, that is a moot point. It's fun to argue on the Internet though.
Someone will propose that the shotgun is the ultimate weapon. Some will say use an AR as easier to use than a shotgun.
But, without a reasonable knowledge and skill base to use any efficacious weapon, you are at a disadvantage. Esp. if you contemplate negotiating around your house at night.
There is little useful variance in your two choices. It probably makes NO difference in a reasonable scenario. If it were more intense than can be handled with a handgun - then you do need the AR.
Thus, that's why folks like Holschen tear their hair out (well, he can't do much of that - sorry -
), when folks in a class just want to talk about ammo and type of gun.
You could handle most situations with a SW Model 10 and a good 38 SPL. If it is more intense, you should know what you are doing. Having a custom 1911 vs. a Glock 34 doesn't matter.