I'll assume you're away from home, hiking or whatever. I've thought about this issue quite a bit. I prefer to analyze real world prior SHTF scenarios. In most recent SHTF scenarios near metropolitan areas (this is the "urban preparedness" room), I generally think it would be advisable to be discreet about any firearms you may be carrying.

In Katrina, the government decided to confiscate firearms. So, if you were carrying openly, you would have had the options of either turning over your firearm or getting into an armed stand off with the authorities. You lose either way. In massive fires in California, you should definitely carry discreetly, and deep concealment preferably (if legal). There are other examples as well.

A SHTF situation would not be the best time to make a statement about your right to carry openly. The authorities would generally freak out in most places, even if you're perfectly within your rights.

The idea here is to survive the situation and not have to turn over your self-defense tool. I think the best the way to go would be a handgun that you can conceal and keep on your person, in your control, at all times. It would be nice to carry around the fire power of a shotgun or rifle, but, again, we're talking about "urban preparedness". The long gun would bring you more troubles, rather than take away troubles.

By the way, I think there are better forums to discuss your firearm options during a SHTF scenario. I suggest you go to a gun-specific site. I'm sure there are quite a few people here who are not pro-gun. I'm pretty sure you don't want to get into a debate about gun control and the Second Amendment.