unless you already own pistols and are comfortable enough to load, fire, and aim them well in a high stress situation, I'd go with the shotgun.
the idea of not having to aim as well is a myth though. at inside-the-house ranges your buckshot pattern will be no more than a couple inches of spread, not exactly a 'hit everything in that general direction' situation.
the upside to a shotgun is you get the combined impact of all of the individual pellets at the same time. but since they are separate they slow down much faster than the same amount of power in one mass. this equates to more 'moment of force' impact on the target (which means it hits harder, but won't penetrate as deep as the same weight/speed of projectile in one piece.) this also means that if you miss these individual pellets will bleed off energy much faster as they pass through walls and such on their way to your neighbors house or your kids bedroom.
plus you really can't discount the motivation for cooperation induced by the sound of a shell being racked into a pump-shotgun.
also your aim will simply be better with the shotgun, you have much more control.
if there is a problem at my house, I grab my pistol. however, when I go out of town and it's just the wife and kids at home, I load the shotgun and put it where she can get to it quickly.