Seeing the evidence is a simple task. Tools found with modern humans are far, far superior to those found with Neanderthals. If you literally want to see for yourself, just go to a museaum (such as the Smithsonian) where you can see artifacts found with Neanderthals and compare them to artifacts found with modern humans.
And of course, if I were being facetious, I would note that modern humans have built skyscrapers and sent spacecraft to the moon in less time than the Neanderthals spent trying to perfect the sharpening of flints..
The Smithsonian is in my back yard so I might have to swing by agian to see if they did indeed have better weapons. My statement was posed in the context of the authors general conclusions - that humans had better technology. I've seen a lot of TV reconstructions on Neanderthal society that stated that they weren't as underdeveloped as the media seems to constantly suggest, which is why the author raised my brow by suggesting that humans had better technology.