I was always of the opinion that, while extremely bleak, Threads was more accurate than TDA.
Although generally I am of the firm belief that the US would come out far better than the UK. The UK is small enough to be completely swamped in fallout after a large scale attack. The US on the other hand has vast tracts of virtually empty land that would not be as affected by the war as the cities.
The one thing that could make matters worse in the US is the Second Amendment. Imagine all of the post-war awfulness from Threads... with guns.
You may be right in a general sense that there will be pockets of the US that remain fairly unscathed, but the great clusters of population in the Northeast, Midwest and Southern California will be decimated, as will most of the major urban areas in the rest of the nation due to their proximity to military installations. The economically productive core of the US would be devastated as thoroughly as anything in Europe. What's left will be lucky to emerge with an 18th Century standard of living.