Neanderthals were superior to modern humans in strength. They were vastly superior. They would make Arnold Schwarzenegger seem like a wimp. The only logical reason for their demise is they were probably inferior in intellect. With superior intellect the weaker modern humans were probably more adept in warfare though weaker in physical strength.
It should also be noted that Neanderthals and modern humans did interbred. We all most fortunately, carry their genes. Neanderthals were human. I think their demise was due to competing with other humans of inferior strength but superior intellect. As Mr. Spock would say, “this is a rare logical thought from you humans.”
The pure Neanderthals were not killed out. They were bred out by assimilation with modern humans. A Neanderthal woman would most logically choose to be the wife (if they had wives then, it was probably mate) of the superior human species. It is all about survival of herself and children. This is just basic human instinct.
Then how do you explain the WWE?
They were not necessarily less intelligent. It could be that modern humans, though weaker, could run faster and further. Look at, and compare, the physiques of track athletes versus power lifters. If speed was also combined with a more accurate throwing ability, a group of modern humans could creep up on a Neanderthal village, hurl a bunch of spears, kill some Neanderthals from a distance, then run away. Repeat every few days, and the Neanderthals would move out of the territory.