The Economist gives us an answer that it loves.
“One theory is that Homo sapiens had more sophisticated tools, which gave him an advantage in hunting or warfare. Another is that the modern human capacity for symbolic thinking (manifest at that time in the form of cave paintings and carved animal figurines) provided an edge. Symbolic thinking might have led to more sophisticated language and better co-operation. But according to Dr Shogren’s paper in a forthcoming edition of the Journal of Economic Behaviour and Organisation, it was neither cave paintings nor better spear points that led to Homo sapiens‘s dominance. It was a better economic system.
One thing Homo sapiens does that Homo neanderthalensis shows no sign of having done is trade.”