Did you see about the crystal stash they found at Ga-Mohana Hill in the Kalahari that indicates the site may have been sacred for, at least, 105,000 years?

That said, I question whether modern man is more intelligent than Neanderthals. It seems more likely that their cold adaptations, which included higher caloric needs, made it harder to compete with us once we invented clothes and expanded into their range. I think we and they were close to intellectual equals and certainly equal enough to have relationships.