It's very easy to completely miss a person under pressure at Home Defense ranges with a pistol. You can put hundreds of rounds down range during practice and perfect your trigger pull, but when the adrenaline starts pumping from life-or-death situations where you have to shoot, your stress-free range funtimes will not help you., You'll slap the trigger and fire with a shaky hand, flinching from the recoil, ruining your accuracy, what you NEED when firing a handgun. Police do it, security guards do it, criminals do it, no one shoots handguns well when fight or flight kicks in unless you specifically train for it.
That being said, a shotgun is much easier to shoot under duress. If you hold it wrong it wont stovepipe, if you pull the trigger quickly/incorrectly it wont go way off target, if you flinch it won't change the impact point, you point and shoot. It's a bit less maneuverable but you gain much more stopping power and reliability under pressure. Long arms are easier to aim with in general as well, you gain a wider margin for error. The first time I fired a pistol I would have put my hands on a bible and sworn the gun had no rifling and misaligned iron sights, that's how much I was missing by. I doubt under pressure I'll be thinking about proper form and 'squeeze, don't pull' and not anticipating the shot, etc. when I'm in a real life or death situation.
I'm surprised no one mentioned the Mossberg Maverick Model 88, it''s reliable and costs less than the Mossberg 500 it's based on.