Humans out of Africa seemed to change spear-point styles over the ages as they tried new things - while Neanderthal humans seemed to be tied to the same styles.
They also may have been nice guys.
History has shown that we are not so nice, and not above pretending to be nice until the nice guys lower their guards.
Disease may have also played a role.
We may have also just out reproduced them. Humans have problems with reproduction due to the large skull, Neanderthals may have had even worse problems. It wouldn't take much of a difference to make a HUGE difference over time.
So what if, every time we come in conflict, they kill us two to one - if our population produces three healthy babies in the time it takes them to produce one.
You are, of course, correct that there are a number of possible explanations for modern humans out-competing the Neandertals, besides the obvious one of us killing them.
The absence of Neandertal male DNA in our own ancestry makes it less likely the process was peaceful, though. That’s exactly what you find in those areas where historically we know the invaders killed all the males and kept some or all of the women.
My point was how often anthropologists jump to the conclusion the replacement of one species or race was peaceful, when there is really little evidence either way. It’s obviously what they want to believe.
BTW, if we’re interfertile with Neandertals, are they really a separate species? Maybe they were just lost Klingons.