The modern world is a human world -- but there was a time when things were less certain. There is strong evidence of
several attempts by modern humans to migrate into Europe before the one that eventually out-competed the Neanderthals. Several recent archeological digs have discovered remains of modern humans from ancient times, but genetic studies of these remains show them to be unrelated to any modern European population -- indicating that their lines of descent ultimately failed.
This raises the question of why their migrations failed, but subsequent ones succeeded in establishing permanent populations. Their stone tools aren't different enough to provide that much of an advantage. So the advantage must've been in something that doesn't leave physical evidence -- perhaps a slight advantage in social functioning leading to better cooperative behavior and more effective marshaling of resources. (This is a very interesting hypothesis, particularly in view of the connection between certain Neanderthal genes in modern populations and the incidence of autism spectrum disorders).