The Idea of conflict or assimilation seems too complex for my taste. I think that the postulated second wave of Cro-Magnon migrants had diseases for which the Neanderthal had little or no immunity.
A more recent example of this would be the Decimation of Native American populations by "European" diseases.
But they lived together in overlapping territory for tens of thousands of years. I don't know about your idea on this one? (maybe?)
Judging from the proboscis disparity it was sniffelus what killed the Neanderthal.