I put down the answer "meaningless." This is for the specific case the OP specified; worst case nuclear exchange in 1962, which means both sides are unlucky in disrupting the other side's best attempts at delivery, both sides are lucky in that their systems work about as well as could possibly be expected. Every weapon built and deployed finds its target as near as possible; neither side stops until all their weapons are gone (except for very small strategic reserves held by the "winner," who would be the USA).
It is not implausible that Soviet bombers would get through, despite the existence of the Air Defense Command. A number of exercises were held to test the state of US homeland air defenses, and in them the "aggressor" forces were able to accomplish a scary number of "hits."
So the USA and other distant Soviet targets would get a nasty hammering.
That said, what the Soviet bloc and China (effectively still treated as a Soviet client, along with I suppose Yugoslavia (or anyway selected points in that country), Albania, North Korea and North Vietnam as well as Cuba of course) will suffer is far worse still. I daresay that the more developed regions of those countries will be rendered not only uninhabited but uninhabitable for generations.
Nevertheless, despite the grim fate in store even for people in nations that would not be targeted at all when the fallout from all these strikes spreads out over the whole globe, I think in this specific scenario, despite being decimated the USA will emerge as still the leading power. However badly off North America is, Europe will be worse off, Eastern Europe still worse. Japan and South Korea, and even South Vietnam and the Philippines along with Taiwan and Hong Kong as well as Singapore and who knows how much of Malaysia and Indonesia will all be targeted, in proportion to how developed they are. I'm not sure if the Soviets will have any firepower left over for India but surely Pakistan will get some strikes, as will Iran and Turkey.
The USA will be much poorer in terms of per capita disposable wealth, far poorer in terms of industrial assets (including farm production as such). But it will be a garrison state, under de facto martial law, and what assets are left will be mobilized for a coordinated recovery/security plan, which means the surviving US overseas forces will more or less fall into line and some of the surviving US home population will be drafted and deployed overseas. In the name of the defense of the Free World, and probably with great sincerity, the Yankees will rule the world.
The reason I said the "setback" is "meaningless" in this context is that it will change over time. Initially, the development of technology will have ground to a dead halt; for decades to come there will be hardly any technological progress whatsoever, and in terms of the amount of tech routinely available to the average person, it will have been knocked down by the war and then deteriorate further, the more so the more developed the nation one lived in pre-war. Except that people drafted into the US military will have weapons pretty much pre-war state of the art, and medical attention probably quite comparable to what they'd have gotten in the Army before the war. The "recovery" machine will prioritize perpetuating itself, and so for generations to come, the costume of the richest people in the world, in terms of how much technology is at their disposal, will be the various shades of US military uniforms. (Making more uniforms is going to be a primary target of the earliest planned stages of recovery!
) Meanwhile the rest of the world will consist of near-dead zones where what life is possible at all is continually poisoned by fallout, luckier zones (probably still suffering visibly from fallout, just not as horribly) left to scrape along with no global economic trade to speak of, and commandeered zones where the US-led coalition is coordinating an prioritizing recovery. Gradually all the less badly off regions get absorbed into the latter, going from being largely left alone to becoming more integrated, which puts burdens on them but also brings some benefits.
Somewhere in there, I'm not sure how to guess just when and where, technological progress will begin again. By the time this happens, the state of the art as of 1962 will be largely restored probably in rough correspondence in terms of world population to the proportions of that year--that is, some people in some regions will enjoy pretty much the same scale of industrial goods as Americans and Europeans did in '62--I'd guess, per military regime rationing, that the range would be more tightly clustered around the average there, with one standard prevailing for most people, and visible privileges for higher rank (civil as well as formally military) being a motive in society but typically involving less actual wealth than in a free capitalist society. But there will be some instances of really tremendous wealth; these will be well hidden. And there will be punitive poverty; some people will simply be left out of the command economy (which would formally be a free market, but under emergency regulation of course) while others--prisoners, dissidents--will be forced labor deliberately kept on low rations and generally restricted. Meanwhile overseas, this pattern will hold with somewhat lower standards of living for the formerly colonial or otherwise Third World.
This being the case, sooner or later, invention and research will find traction. Probably much of it would start in military labs, and other instances would be in the civil recovery effort, attempts to solve problems and cut through bottlenecks.
In addition to some decades or generations being lost, the recovering world would also have I suppose a seriously decimated population. The First World nations will lose hundreds of millions in the immediate war, then comparable numbers or more will "die back" in the disrupted and fallout-poisoned aftermath. China of course will be heavily targeted and its industrial centers most of all. India won't have dieback except insofar as fallout poisoning causes it, unless the Indians attempt to use their relatively unscathed status to project power to preempt the US military led "plan." Then--well, we might just concede the region around the Indian Ocean to them and try to take them on as partners, or there might be an ugly WW4 to cut India back down. Note this a decade before India developed her own nukes OTL; with the war having happened it seems unlikely they can have a deterrent force any time sooner whereas a small strategic reserve, which the US junta is sure to start rebuilding as a top priority right up there with minimal rations and uniforms, would be enough to cripple India industrially.
So I'm not sure about South Asia, but by and large the most populated areas before the war are depopulated, and even with crazy natalism, it seems likely the next generation will suffer low or even negative growth, even after the years or decades of severe dieback are over. The upshot then might be a world where India dominates the planet in terms of population, but the Yankee-run junta still holds more wealth.
So India may have the population but with a lower per capita wealth than OTL (not having the rest of the world to trade with) while the "West" has the technological lifestyle but much fewer people than OTL. These factors will inhibit the rate of technological progress. But eventually, the pace will match and perhaps surpass that of OTL; in some ways, fewer people means more resources to go around.
My guess then--a "Dark Ages" lasting 20 years or so, in which very little progress takes place. Then a 30-50 year period in which the pace starts to pick up but does not match OTL rates until the end of it. So in 1980, the world is less capable than in 1962 but roughly the same per capita. By 2030 pessimistically, or by the year 2000 optimistically, the general range of capabilities is similar to that found OTL in the mid-1980s. This assumes that India makes a demographic transition to stabilize its population around a billion or so.
So in terms of the overall delay, seen by ASBs who can compare OTL (assuming we don't run into some civilization-wrecking catastrophe of our own, which unfortunately looks like quite an assumption) a century hence, the wartime TL is delayed 20 to 50 years, which I note is in the popular ranges. But even in the optimistic scenario that has a return to "normal" rates of development by 2000, the period between the war and the "return to normal rates" year involves much worse backwardness; technical knowledge does not vanish, it is sequestered in refuges, but most people don't benefit from it and as an average their lifestyle slips back decades or even centuries during the Dark Age. By 1980 or 1990, the worst of that is over with one hopes and things get back to pre-war levels, then eventually at 1980-1990 levels (but in 2000 or even 2030 or later) the pace of progress resumes with that 20-50 year backwardness--and conceivably in the ATL, if the world population is a lot lower at that point, progress actually starts to happen faster, so the gap gets closed completely and the ATL pulls ahead sometime late in the 21st century.
So, there isn't one number that characterizes how far back most people's lives have been set. Remember, most people in the developed world either die in the war or its aftermath, or have to fight to survive those years--quite a lot of lives are set to zero. Some of them will live through decades of 19th century or worse conditions before the recovery regime gets around to incorporating them on 1950 (Spartan, army boot camp sort of standards) terms, then more years while things improve back to 1960 levels (lower class rationed). Few who saw the war year will live to see an OTL 1980 lifestyle. But by 2020 the world will seem pretty "normal" again; the war an overshadowing historic memory, perhaps institutionalized in a world regime organized along planning and rationing for the public good, but that itself will seem normal and reasonable to this generation. (Unless one foresees some kind of anti-regulatory revolution). Eventually the "decades we are behind" number might shrink to zero and become negative.
This situation holds if the war happens in 1962. If the war happens in 1972, I'd be much less sanguine the USA could ever recover. The Soviets and Second World in general would be even more trashed--but the fallout from it would be even more devastating. I think sometime in the 1960s we crossed the boundary where total war would mean a definite Dark Age in the sense that most of humanity, even in nations not primarily targeted (there are so many weapons though that every nation is probably going to get at least one or two strikes, at the capital if nowhere else) will suffer severely, dieback will wipe out most of the population, and the relatively few survivors will overwhelm whatever token centers of recovery might manage to survive being targets in the war, leading to total breakdown of all would-be technological centers. In that case, the answer would be measured in centuries, I'd guess half a thousand years or more, and since the later the war happens, the more depleted the world's easiest to acquire resources become, making an eventual renaissance of industrial civilization harder to accomplish. So even after hitting bottom and the slow beginnings of recovery, from a much more devastated global ecosystem that itself is recovering slowly, the pace of progress must be slower indefinitely. The number starts at 500 or so, and keeps slipping ever farther back.
If the war happened in 1982, we might be looking at the immediate death of a third of the world population, followed by dieback of 90 percent or more of the rest, and a thousand years or more before a new industrial civilization is possible. If the Cold War continued to 2012 and then went hot, the proliferation of targets due to the rising world population and the cumulative consumption of easy to access resources might prevent industrial civilization in any form from ever rising at all, if the sheer gigatonnage of weaponry extrapolated from another 20 years of gung-ho Cold Warrior arsenal-building is not quite enough to totally exterminate our species from the fallout alone.
On the other hand, if the war happens in 1952, I suppose that Europe, especially the East of it, is badly trashed as is Japan and both Koreas while the new PRC loses all its industrial centers. The American arsenal of that year would be enough to do quite a lot of damage. But would a US-led coalition, particularly since its potential partners in Europe are themselves decimated, have the ability to impose a new government on the territory of the USSR, still less, on China? Sooner or later those peoples would rise up and probably with a revanchist regime--there would be a World War IV.
So overall, I guess that 1962 is about the "optimum" time to have a nuclear exchange. It punishes the Americans enough that we'd have a different sort of regime after than "business as usual" and takes the Soviets out of the picture completely (not China though, not in the long run), but the world has enough untapped resources and the general level of devastation is sort of recoverable from. Earlier, and you get second rounds of war. Later, and the war breaks civilization.