Crosshair
No offence, but in a SHTF senario, I doubt they are going to bug you for carrying a rifle as long as you are not thretening anyone. I would probably carry my rifle slung over my back or against my shoulder. One looks much less threatening that way.
I hate to disagree with you but I think that would depend on the situation. I NOLA right now I don't think being seen with ANY weapon at this time is a good idea. At least if by "this time" we mean when the military units position themselve to quell looting and street violence. I can easily see an "aprehend and/or disarm" policy going into place down there. Martial law has been declared so that whole "rights" thing doesn't really count right now.
And as for the origional question, I'd vote rifle. I have several rifles and shotguns, all in a variety of configurations. For in house protection I've got a shotgun because I know my range is going to be under 30 yards, without question.
But for general purpose SHTF when I don't know the exact cercumstances I may face I'm going to have to vote for the rifle for all the reasons already given. Range, loading speed, accuracy, ammo volume. And here's one nobodies talked about yet. What if your 75 yards away and your intended target has non-hostiles near them? You can't use buckshot without fear of hitting an inoccent. I know the answers going to be slugs but as has been mentioned before, now you're just using a large bore rifle that kicks a lot.
I love how everyone talks about the "versatility of ammo" for the shotty. So if you're in NO right now what are you going to do? Keep slugs in your front pocket, 00 buck in your back pocket, field loads in your socks, and specialty ammo taped to your hat? And would you realistically plan on wandering around with 4 boxes of shells? Thats a lot of weight and only 100 rounds. I could fit 90 rounds for the AR into 3 mags in a single ammo pouch and another 30 in the weapon.
Now if the situation was general purpose subsistance hunting with self defense as a secondary concern then I think a shotgun is an exellent choice. But for a primary defensive weapon I'd go with a good rifle.