The common counterargument to long arms for home defense is you can't use it with one hand, which may be needed if your other hand is busy calling 911, using a flashlight (could be mounted on the gun, that's another debate), carrying a child, dragging an injured family member, grappling with an intruder, etc etc. They are also easier to maneuver around corner and through a house.
The long arm is great if you can dig in with it until the police arrive. But if you need to move about the home for any reason, I think the handgun is probably better for MOST people. Otherwise I am hiding behind the bed with the 870 until I hear sirens.