I think what gives Threads extra psychological heft is the fact that it opens with a very long sequence of everyday life pre-bomb, which grounds the film in reality. Because the cause of the disaster is unknown, it is easier to shrug off "The Road" as an alternate universe. The events in "The Road" are more awful, but less immediate. Now that I think about it, that grounding also enhances the "Wizard of Oz", in a different way.

I think the factor that made Threads so powerful, particularly if you saw it in the early 1980s, was that appreciating how close we were to that scenario actually happening.

The Road is, I would agree, rather more bleak but as the threat is rather ill-defined it doesn't quite have the same sense of dread, at least to me.

However, I was 18 when I saw Threads for the first time and it did rather leave a a mark, as did the related "QED: A Guide to Armageddon" which is a chilling look at the effects of a nuclear weapon on a large city.

https://www.youtube.com/watch?v=9GJttnC8PoA

The bit where the effects of the heat of a nuclear weapon are shown on meat in a butchers window (around 6:40) literally gave me nightmares.