From the Economist article:

Previous genetic analysis, which examined DNA passed from mother to child in cellular structures called mitochondria, had suggested no interbreeding between Neanderthals and modern humans. The new, more extensive examination, which looks at DNA in the cell nucleus, shows this conclusion is wrong. By comparing the DNA of Africans (whose ancestors could not have crossbred with Neanderthals, since they did not overlap with them) and various Eurasians (whose ancestors could have crossbred with Neanderthals), Dr Paabo has shown that Eurasians are between 1% and 4% Neanderthal. That is intriguing. It shows that even after several hundred thousand years of separation, the two species were interfertile. It is curious, though, that no Neanderthal mitochondrial DNA has turned up in modern humans, since the usual pattern of invasion, in historical times anyway, is for the invaders’ males to mate with the invaded’s females.

Duh. The Neanderthals were way stronger than us, and a Neanderthal female would kill a Homo sapien male who tried to rape her, and literally eat him for lunch.

According to Rosas, there is evidence of cannibalism in Neanderthal remains from other European sites. "I would say this practice... was general among Neanderthal populations," he said.

If Neanderthals ate other Neanderthals, then they would certainly eat Homo sapiens.

Despite being as intelligent as Homo sapiens (up until around 45,000 years ago when Homo sapiens surpassed them, known as the Great Leap Forward), they were brutal beasts who would rape and kill Homo sapiens they came in contact with. This explains why no Homo sapiens existed in Europe until about 45,000 years ago. But when Homo sapiens learned how to use throwing weapons, and became smart enough to use smarter tactics against the Neanderthals, then they conquered Europe and over the course of the next 10,000 years wiped the Neanderthals out of existence.