unless you have a concrete house that is reinforced, or a bomb shelter in your basement, id bug out. bugging out is more annoying, no doubt, but you have endless options and can really go somewhere remote where no one in their right mind would come looking to steal things. the problem with any house in any semi metropolitan area is that there will be a lot of looters and it won't be that long til they come for you. even if you have guns to protect yourself, people can just burn down your house. it would be hard to make the decision because i would want to hold out as long as i could, but frankly if you wait too long you may then be stuck.

if you are bugging out though you need specific supplies. i have a large tent that is 12x12x8 and allows a wood stove. my stove is a good quality, air tight one that can heat a 12x12 to a comfortable temp down to -30. it can handle wind and snow. so in theory, as long as i can cut wood down, i can survive the elements. i also have cots, heavy duty fleece lined below 0 degree sleeping bags, coolers, guns, ammo, axes, sharpenders, etc. i also have some long term storage foods. all of this stuff fits in my suv. as long as i can find small game and/or fish and am located in a wooded area (both of which are likely) i should be able to make it indefinitely. its not as comfy as a home no doubt, but its awfully safe.

all that being said, when i build a house i will likely build a bunker in it. they aren't much more expensive, easy to hide, and can be pretty self sufficient if you do it right. in that case i would stay.