If it's either/or, I'd go handgun...you can take it out and about with you almost anywhere when that becomes necessary (assuming it's legal in the given jurisdiction)...you can answer the door with it discreetly without getting an aggravated assault charge from whomever's on the other side of the door...and if you have to go mobile inside the house, it leaves a hand free to hold a cell phone or do other tactically useful things.
I personally suggest and handgun AND long gun approach. The handgun is "infantry", when you have to move, as in the situations above. The long gun is "artillery," when you've barricaded the family and want serious firepower to wield against whatever is kicking down that last remaining door between you and the intruders.
The maneuverability of the Short-Barrel Rifle is only an advantage when you're doing a building search, which is almost never a wise move for the lone armed citizen. It will be particularly loud when it discharges in close quarters such as a hallway, loud enough to cost you some hearing if you don't have ear protection. Finally, since there are many PRO-gunners who don't realize it is legal in many states for you to own SBRs with ATF licensing, you can expect ANTI-gunners in the prosecutor's office, or on the jury, to go nuts about you using a "sawed off gangster rifle" or some such BS.