Well, we humans are a bunch of brutes. It's up to you to take that as a negative or a positive description. I personally accept our flaws, our warlike tendencies, as things that allowed us to become the dominant species on the planet. It is our flaws that make us whole beings; perfection would only lead to hubris. Vive l'humanité!
In any case, it is quite unlikely for the Neanderthals to have a perfectly harmonious society and inhabit the entirety of the Earth. In order for them to dominate the planet as we do, they would have to radically change from their historically environmentally-conscious and relatively conservative natures, and become as violent, as innovative, and as open to social change as we humans are. So, they would have to become just like us, and would never remain as they were.