In a nutshell [so the theory goes], Homo sapiens could hunt by ambush or by long distance pursuit, while the Neanderthals were only adept at the former, as they weren't good runners because of their heel structure. When the last ice age hit Europe turning the forests into tundra, the ambush strategy didn't work so well, and the Neanderthals couldn't adapt.
For the details:
http://www.newscientist.com/article/...in-a-race.html
Would anyone care to poke holes in this idea?