You assume that the Neanderthals weren/t the smartest and most peaceful of the two groups. It takes more brains to live in cooler climates than warmer climates such as africa dear.
The Cromagnon Man lived in Europe the same as the Neandrathals. And about the same time. But the Cromagno outlived the Neandrathal man but both went extinct. But the Cromagnons lived in a wider area than the Neandrathals did. They ceased to exist about 10,000 years ago. While the Cromagnons resesembled Homo Sapiens they were replaced just like the Neandrathals. Cromagnon's DNA stopped cold while the Neandrathal DNA is still in all of us. It appears Homo Sapiens bread the Neandrathals out of existance while the Cromagnon just stopped.
BULL. Stick to topics you know something about, if any. Cro Magnon did not "die out," it is simply an archaic term now for what we realize is really an anatomically modern human without enough of a difference to distinguish from anyone else. Cro Magnon did not fade away like Neanderthal which was a wholly different line of Hominid, he simply evolved farther into what finally became distinguished as modern man. And since he cohabited with homo neanderthalenis, they no doubt interbred, neanderthal interbred with Homo, and there is undoubtedly strings of Cro Magnon today in all of us.