Cro-Magnons (modern humans) have ALWAYS had the image of the Neanderthal as the proverbial "caveman," grunting and snorting whilst dragging off a female to his den by the hair. (Don't get too excited, guys) The Neanderthal man--- brutish, stupid, & mute.
In my opinion, this image of the Neanderthal man stems from a deep-seated inferiority complex on our part. Perhaps, like the interaction of the Europeans and Native Americans, the so-called superior race was actually the more brutish and stupid.
Anthropologists know the Cro-Magnons and the Neanderthals co-existed in Europe for more than 15,000 years. No doubt there was extensive interaction and perhaps intermingling. Why did the Neanderthals die out (except for a lagging mixture of Neanderthal DNA in Modern Europeans (especially redheads-- controversial opinion)) ?
In some ways, the Neanderthal had a survival advantage over Cro-Magnon. They were in Europe for many thousands of years. The Neanderthal had already proven they were hardy survivors in a harsh environment.
But the Cro-Magnons won out, presumably, because of intelligence & language.
Now DNA research suggests the Neanderthal had language too. A genetic marker for speech & language-- FOXP2-- has been found in Neanderthal bones. http://www.msnbc.msn.com/id/21362048/ Other evidence for speech, such as a hyoid bone, a hypoglossal (tongue) muscle, & similar auditory sensitivity, exists. It is likely the Neanderthals did have language. In my opinion, they could not have survived for all those years without advanced communication of some sort.
Cro-Magnons were not necessarily superior in any way, but more adaptable. In a sense, the Neanderthals were overachievers. Their people managed to survive in an extremely limited environment. When that environment rapidly changed, due to climate, or influx of disease, or lack of game, the Neanderthals could not adapt quickly enough.
The superior (more numerous) gene flow of the Cro-Magnon eventually blotted out the Neanderthals.
Yet they remain our human cousins, our closest competition for ruling the planet.