Neanderthals faced a different species of humans whose culture they were not capable of integrating into. Humanity right now forms one unified global culture through which ideas and technology freely flow. The rising tide of technology is lifting all boats (massive wage growth globally).
Moreover, it's not clear that your premise is accurate. Neanderthals constitute 3 percent of Eurasian human genes, meaning that their genes were evolutionarily successful (3% * 6 billion > 100% * 100,000), and this is ignoring the success of their close kin, with whom they already shared >99% genes.
Moreover, it's not clear that your premise is accurate. Neanderthals constitute 3 percent of Eurasian human genes, meaning that their genes were evolutionarily successful (3% * 6 billion > 100% * 100,000), and this is ignoring the success of their close kin, with whom they already shared >99% genes.