The most pressing question along these lines would have to be who would win a fight between The Situation and Pauly D? The answer? The audience. And the gene pool of the human species for ridding itself of at least one of these guys.
If you read the whole thread, you'll see we've already covered the total folly of assuming that evolutionary competition is as simplistic as a literal, universal fight to the death. The notion that one species winning out over another is a matter of combat is a sensationalist caricature. It's more about different abilities to adapt to their environments, different lifestyles and technologies that make one population better able to feed itself or less prone to disease or more able to adjust to a climate change. Indeed, there can easily be circumstances where greater aggression or fighting prowess is a negative survival trait in the long run -- for instance, in situations where cooperation is a better survival strategy than conflict. Humans thrived as a species because we cooperated with one another, because we evolved to share our resources and strengths and knowledge and skills and thereby keep more of our people alive than we could if everyone just fended for themselves. Aggression is a tool in the kit, but it can't be the only tool a species has at its disposal. Overspecialization is rarely a good evolutionary strategy.
^Exactly. There are thousands of endangered species that are not dieing off because we hunt them to oblivion, it is because we take over their habitat. As one possibility, let's suppose that Neanderthals need far more calories to stay healthy. Expanding human populations and then a severe famine could have drasticly affected the Neanderthals far more than humans. Another possibility is disease, humans could have carried a virus that was an annoyance to us, and deadly to Neanderthals. It could have been the common cold, as in War of the Worlds.
Whatever gave you that idea? A decades-old textbook? That notion is way out of date, as we have already discussed extensively in this thread.
Here's an article on some recent scientific research on the differences between modern humans and the extinct Neanderthal and Denisovan groups: http://io9.com/5939148/new-dna-evidence-could-explain-what-happened-to-the-neanderthals Scientists analyzing the genomes of the different populations found that many of the key genetic differences between our genome and theirs are in genes having to do with brain development. That suggests that we outlived them because of some difference in the way we think. Perhaps it was the same kind of changes that enabled us to develop more elaborate social structures, technologies, language, etc. and thus be better suited to withstand climate change and disease, better at obtaining a steady supply of food, and the like.