From Scientific American:
X-Men: First Class, like earlier movies in the series, repeatedly invokes the idea that its mutants and humans are engaged in an evolutionary struggle for dominance like the one between humans and Neandertals thousands of years ago. Professor Xavier and Magneto talk about the Neandertals having resentfully looked at the superior new species moving in, and the moderns having displaced and slaughtered the older species. At least this movie has the excuse of being set in 1962, when such ideas about human evolution were more common. Neandertals were then typically portrayed as a species of mentally inferior brutes who could not compete with the smarter, more technologically and culturally advanced Homo sapiens who evolved later.
But today, the paleoanthropological picture of the relations between Neandertals and modern humans is completely different. Skeletal reconstructions show that Neandertals had brains larger than our own, and archaeological digs reveal that they had a distinct culture but sometimes used some of the same tools that our ancestors did. Indeed, studies published in 2010 by Svante Pääbo's group at the Max Planck Institute for Evolutionary Anthropology in Leipzig concluded that several percent of non-African people’s genes came from Neandertals, so Neandertals may not even have been a species apart. Most important, little evidence supports the idea that Neandertals and modern humans were in much open conflict. During the last ice age, Neandertals may simply have fared poorly and gone extinct largely on their own, with modern humans later occupying their old territories and perhaps breeding with some stragglers. One recent controversial study has even suggested that Neandertals were essentially gone from Europe by 40,000 years ago, thousands of years before modern humans arrived. In any case, Professor X and Magneto had it wrong.