really neither. Hollywood likes to portray these dog-eat-dog lone ranger scenarios, but the reality is people band together.
A good many major cities would be decimated, but even just an hours drive away you'd be mostly fine, at least after a week or two when the fallout has fallen out.
I don't mean to downplay an all-out nuclear exchange as no big deal, obviously it would be an even worse disaster than ww2 etc, but it wouldn't end civilization let alone all life.
there is an awful lot of misery that would happen for a few decades
this isn't going to be Fallout 3, it's going to be The Road for a few decades.