Home protection guns ultimately are personal preference. This is an argument that will never be settled. What's good for me my not work for the next guy. But there are some hard facts that can not be disputed.
1. It is easier to maneuver in close quarters with a handgun. Long guns are.....well...longer
and just by the nature of the beast harder to maneuver.
2. A shotgun w/ bird shot will have less wall penetration than 99% of handgun rounds. The smaller the shot the faster it looses energy and the quicker it will spread.
3. An ounce of lead is an ounce of lead. Birdshot is just as lethal as buckshot at close range.
Don't just take my word and don't believe what anyone else rights, go out and do it for yourself. As a full time LE firearms instructor I am lucky enough to have the time and resources to go out, build walls (exterior type and interior type) and shoot holes in them. Recover the rounds when possible examine what they do, how they react to different types of barriers. You don't have to have a job like be to do it. Anyone can build 2 X 4 walls with sheetrock or siding with insulation, and go to the range and shoot them.
Stay safe and fight to win.