Fundamentally, it’s a “here be dragons” situation. We just don’t know exactly how many of the systems - mechanical, human, and natural - will react to a large-scale nuclear war. How many warheads successfully launch? How many detonate? Against what target sets? How many cities see firestorms vs how many do not? How badly are communications hit? How much ash can the atmosphere take? This is just a fraction of the legions and legions of unknowns clawing at the gateway.
Because of this, I see the post-nuclear environment in a large-scale exchange as a curved sliding scale of possibilities. Call it the "nuclear horseshoe" if you will, at least as far as probability goes. On the far end of the scale, you have "total human extinction" from all the second-order effects: nuclear winter, disease outbreaks, famines, civil breakdown, etc. On the near end, you have a "brokenback war" scenario, where due to a variety of factors, the nukes maul the countries involved but don't actually collapse them (at least... not immediately), leaving them with just enough to sort out the remains and keep fighting. Both of these are possible - in so far as we can tell - but seem unlikely.
Between these two improbables we have varying levels of national/societal collapse, with all the attendant human dieback that entails. This could range from only the directly engaged countries collapsing, to second-order effects collapsing every nation outside regardless of proximity to the war. Most likely, what we'd see is something of a mix, with all the directly involved countries collapsing, second-order effects collapsing a number of the not-directly-involved, and the rest experiencing some period of instability, hardship, and probable reduction of living standards and technological base before managing to orient themselves. Naturally, the largest and most powerful of the survivor states in that last scenario would be the best positioned to dominate the post-nuclear world. Who they actually would be is a matter of speculation.