To be honest, those skeletons don't look that much different to me. What was it that made modern humans superior to Neanderthals so much that Neanderthals died out?
Its hard to tell from the diagrams but the Neanderthal skeleteon is much larger and thicker. From a design perspective, it looks like a structure that was designed to take a beating. But studying a fossil can only tell us so much, I'm sure that there was a lot more to the rise of humans than just bone size.
I once read an interesting hypothesis that suggested Neanderthal, because of his larger brain case, didn't have enough room in his mouth for his wisdom teeth. This would have caused severe dental problems.
On the other hand, I wouldn't dismiss the possibility that the two subspecies simply assimilated one another. There really wasn't much difference between them, other than some very small morphological factors. And just as a wolf has all the genetic factors needed to make a poodle, Neanderthal might simply have evolved into a type indistinguishable from what the paleoanthropologists like to think of as "modern" man.