There's not a lot of evidence for a "war" especially since most of us from non African decent have measurable amounts of Neanderthal genes. It's just hard to stay alive when you go to the berry bush only to find that tribe of weirdos already ate all the fucking berries. Breakfast is ruined because the weirdos also already stole all the birds eggs. etc..
But when we're trying to fish at the same time the weirdos sure look hot wet and naked.

Thanks! Very interesting. From other reading, there was a lot of cross breeding going on as well. Perhaps the homo Sapiens genes were more dominant and helped in the overtaking of the Neanderthal spiecies?

Some theories are that Neanderthal actually assimilated and mated with modern humans. Other theories are that they were wiped out by a pandemic that Cro Magnon was immune to. Some say they are still here wearing MAGA hats.