Native Americans were hardly the peace-loving enviro utopians as some try to portray them. They were extremly violent towards each other as well. No particular knock on them, that’s just human nature deep in the genes - a fear of someone who isn’t part of your tribe, bred that way for good reason - because in the past, someone who wasn’t part of your tribe often represented a mortal threat.
It wasn't fear, it was practicality. When your tribe expands beyond the supporting capacity of your territory, the only way to avoid starvation is to invade your neighbor's territory.
As far as how Cro-mags killed off Neanderthals, a moderate advantage in speed or throwing ability translates into a BIG military advantage. If you can creep up to your enemies, throw spears at them from longer range than they can throw back, and then run away faster than they can follow, it would not take long to wipe them out.