evidence suggests that Neandertals were pretty thoroughly carnivorous, which may have been one of the reasons that H.Sap. was able to outcompete him. If that is the case, you're not going to get more than hunter-gatherer (or rather pure hunter) societies, and you're not going to get settlements.
While you probably wouldn't get agricultural societies in the Neanderthal World, you'd likely, IMO, still see pastoral/herding societies. This could lead to some form of "civilization". Certainly shared cultures, possibly even sprawling "steppe nomad horse cultures", though probably not stationary urbanized cultures...unless someone gets the idea to grow fodder for their herds. There may end up being semi-permanent seasonal settlements near major resource areas, however. Perhaps these along with ""stock fodder" agriculture, could lead to some form of urbanization.
Or maybe they just turn into hippie-dippy-Darwinist eco-friendly gender-segregated free-love technotopias!