The Neanderthal was very much a hunter gatherer and all tht which it entails. Modern humanity was much better at that and mostly absorbed the Neanderthal into a much larger population. It really is that simple and the same has largely already happened to North American First Nations although immigration has brought that about. Of course, immigration did it for the Neanderthals as well.
Humanity simply knew how to support large villages.
In the meantime they also shared the capacity to make some form of images for their own intentions. This is at least confirmed now and we can dispose of any remaining efforts to downgrade their mental capacity as likely rubbish. These folks hunted successfully with robust spears.
Newly Discovered Engraving May Revise Picture of Neanderthal Intelligence
Carved grooves hints at abstract thought among these extinct early humans.