There's a theory that we didn't actually "defeat" the Neanderthals, but rather mixed with them. Around 2% of European DNA comes from Neanderthal ancestry. The idea is that when humans coming from Africa encountered the Neanderthals, they started interbreeding. Over time, Neanderthal DNA gradually faded until everyone became fully human. In other words, it wasn't a war between humans and Neanderthals. It was multiple generations of interbreeding until pure Neanderthals eventually disappeared.