The first specific nuclear gene variant retrieved is one that prior studies have linked to language and speech in humans and suggests Neanderthals had the capacity to develop speech.
Have you ever read the Clan of the Cave Bear books? They're all about the differences between neanderthals and cro-magnons. They're fiction, but the author does a mighty hell of a lot of research- a new one comes out every ten years or so. They're good reads.