A long arm may well be more effective than a handgun for defense. The issue is whether the defender can access it instantly from wherever he or she may happen to be \in the event of a sudden violent and forcible entry.
The idea of using deadly force to defend "property" is not a good one. It is unlawful in a all states but one, and is generally not a sound strategy in th one that does allow it under very limited circumstances.
The shotgun is not superior from that standpoint at household distances.
The results of that "simple experinent" tell us very little that is useful.
The boldfaced text above is a key issue.
I actually experienced a "sudden violent and forcible entry" when someone started kicking our kitchen door down about 20-ish years ago. At the time, I happened to be awake and sitting in a chair about 20 feet from the door being kicked down.
My shotgun was in a bedroom closet at the other end of the house. I had to run to that end of the house to get to the shotgun, and then run back. By the time I got back, the door had given way.
At this point I didn't know if there was now someone in the house, because I was not able to see the door while I was running to get the shotgun. This was about 1:00 AM in a very obviously occupied home with lights on and 2 cars in the carport. Generally burglars looking for property don't break into occupied houses, so I was rightfully very fearful of our safety.
As luck would have it, it actually WAS a property crime - a smash-and-grab purse snatch of my wife's purse that had been sitting on the kitchen table, and the burglar had grabbed it and ran to his waiting getaway car and sped off.
But if it had been something else, I would would have been in a race with a bad guy behind me to get to that shotgun.
I still have that shotgun in the same closet, but ever since then, I have made sure that I will never have to take more than a few steps to be armed. It is much easier to wear a handgun on you, or have it stored nearby, than it is to carry a shotgun around.