Humble opinion. With a rifle you have more rounds, with a shotgun you have more firepower. More projectiles on tap, and more projectiles per trigger squeeze than anything short of a fully automatic weapon. The shotgun is much more lethal (read "likely to solve the problem the first time") than any rifle round. If I'm in NOLA right now, by myself, I really don't care about the guy a football field away, and if he develops an interest in me I'm more than willing to run or take cover. I engage nothing where I don't have a n overwhelming advantage and no other alternative. At some point law and order will be restored and I'd rather not have explain why I was the "crazy gunnut sniper" who was picking off people from the next block over. If the BG is really interested and decides to close, every step inside 100 yards increases my advantage. To quote Alonzo Harris' shotgun quote, "...You know I'm surgical with this bitch, Jake." You can pattern slugs out of a rifled barrel into a 3-4 inch circle at 100 yards, that's good enough for a headshot, which is why I don't care that much about armor penetration. If the discussion takes place at closer ranges, while I'm sure he'd see your point after a couple three 5.56 rounds, the first load of buck center mass pretty much settles the argument. The amount of ammo one can carry is a definate consideration, but reloading isn't. With a shotgun you don't have to replace clips, just top off the tube on the move as you expend rounds. Therefore unless you have to simultaneously address 6-7 targets (and if you do, you might want to consider tweaking that part of the plan), until you run out of ammo there's no reason to ever have an empty gun. You can't effectively lay down volume fire with a shotgun, but since the last time I suggested that as a tactic I was widely shouted down, I'm assuming that's not a consideration.
Now all that becomes completely invalid if a) we're talking a multiperson survival cooperative, since then you can specalize weapons so i'd essentially have both, or b) permanent breakdown/no reasonable timeframe on the restoration of law and order, which would call for a more offensively oriented stance... and a real rifle round like the .308.