Concur. But its the why that is the question isn't it? I have often wondered if it doesn't have something to do with our arrested development. A 1000 pound animal can grow to adulthood and reproduce in two years, yet we take around 13 years to reproduce and fully 20 to reach adult maturity. For bare survival of the species, a short growth cycle is a powerful tool. A day old calf can be caught by a man on foot, but a three day old calf cannot. Human babies are essentially helpless for years, while they program their brains. If Neanderthal matured more quickly, they might survive better in very harsh environments, but never have the time to program those big melons. I'm aware of recent tests that say this isn't the case, but I wonder how conclusive those are.
I think small differences can make a huge difference in the aggregate. Think of economies of scale as an analogy.
One good example is 'altruistic' behavior; the willingness to help a fellow in need. A chimpanzee will generally not help another in distress even when it would cost itself nothing. Humans obviously will help another human in distress, often at great cost to oneself (even to the point of outright sacrifice of one's life).
So, if Neanderthals were less inclined toward altruistic behavior, that would make a difference over time. And that's just one trait.
The objection can always be raised that this is all conjecture or 'just so' argumentation, but here's a fact: We're here; Neanderthals aren't. Obviously we were better at whatever it is we needed to do to make that so.
That's a good question, how they vanished completely. I'm thinking it had to be a serious plague to which they were vulnerable while our guys were not. Maybe related to cannibalism.
Otherwise---such gradual marginalization that eventually they were left to small isolated areas where inbreeding and its nasty social dynamics did them in. I think they had some sort of culture that broke down, and that alone can kill off a community, no plague necessary.
Still the question remains, since 100% gone (after that successful long run) does seem awfully strange. It's just that we are thinking in terms of the "last man" among them, and actually we have to think of the last community. Once the "community" has collapsed, from a social unit to mere numbers of individuals (every man for himself), the process of extinction speeds up real good.
That raises the question of why did they develop all that cranial capacity if it wasn't put to use.