Why did our species survive, not the Neanderthals?

Interesting article in New Scientist on Neanderthal extinction. It directly contradicts something I thought about Neanderthals and technology / tool creation so I must have a look into it to see if this is something under debate or if I should be changing my mental model.

"The history of the Neanderthals isn't a Brothers Grimm fairy tale, but much of what has been written about the ancient human species may as well be, says evolutionary ecologist Clive Finlayson in his informative monograph...

"None of these just-so stories quite add up, Finlayson says. There is no clear indication that Neanderthals were any less intelligent than H. sapiens, and genetic evidence has shown that they share with humans key changes in Foxp2, a gene involved in speech and language. The distinction between Neanderthal and human technology isn't as clear-cut as palaeoanthropologists sometimes suggest, and Neanderthals hunted smaller game and seafood where it was available. Meanwhile, a first-draft sequence of the Neanderthal genome offers no sign that they contributed to our gene pool."

Article - 08 November 2009 - New Scientist.