But while Neanderthals would have had a variety of personality types, just as we do, their way of life would have selected for an average profile quite different from ours. Jo or Joe Neanderthal would have been pragmatic, capable of leaving group members behind if necessary, and stoical, to deal with frequent injuries and lengthy convalescence. He or she had to be risk tolerant for hunting large beasts close up; they needed sympathy and empathy in their care of the injured and dead; and yet were neophobic, dogmatic and xenophobic.In other words, the European Neanderthals were conservatives, while the out-of-Africa hominids were liberals. Plus Neanderthals were ugly. Or so they imagine.
So we could have recognised and interacted with Neanderthals, but we would have noticed these significant cognitive differences. They would have been better at well-learned, expert cognition than modern humans, but not as good at the development of novel solutions. They were adept at intimate, small-scale social cognition, but lacked the cognitive tools to interact with acquaintances and strangers, including the extensive use of symbols.
Update: The NY Times reports that the out-of-Africa theory has been superseded:
The new view is fast supplanting the traditional idea that modern humans triumphantly marched out of Africa about 50,000 years ago, replacing all other types that had gone before.
Instead, the genetic analysis shows, modern humans encountered and bred with at least two groups of ancient humans in relatively recent times: the Neanderthals, who lived in Europe and Asia, dying out roughly 30,000 years ago, and a mysterious group known as the Denisovans, who lived in Asia and most likely vanished around the same time.