Sub-Saharan Africa is almost entirely free of Neanderthal DNA except for some groups who acquired a bit through introgression from Eurasian modern humans.
Various sources of Archaic admixture have been observed or postulated for different modern human groups; determinations about their similarity to modern humans are made in broader grounds. As a practical matter, taxonomic distinctions between different hominid species/subspecies are generally retained until sufficient evidence accumulates to justify dissolving the boundaries. The idea that archaic groups like Neanderthals were very cognitively sophisticated has been around for a long time; the question is whether it is more informative to maintain them as different taxa.