Anthropologists estimate that the Neandertal population never was more than about 25,000 at any one time so they were quite widely scattered. You are correct that their last stand seems to have been in Spain in the region of Gibraltar but IIRC it was more like 30,000 YBP. Just why they went extinct is still not settled but it seems likely to me that modern man simply pushed them aside in some way.
What we've learned about Neanderthals from their artifacts and their skeletal remains, is that they were surprisingly similar to modern humans. They wore animal skins, used fire and had stone tools and weapons, created cave art, played crude bone flutes, probably had a spoken language (they were according to most anthropologists anatomically capable of speech), apparently traded goods between different clans, and they buried their dead. If I'm not mistaken, science also maintains their brains were either larger than modern man, or around the same size.
The prevailing theory is, that Neanderthals (being much stockier and slower) than modern humans simply were not able to compete with modern hunters. After the last Ice Age, huge slow creatures like Mammoth Elephants were replaced by faster moving, smaller game. Not exactly good targets for Neanderthals wielding large heavy spears. For example, the same decline occurred in the early American Indian population, when buffalo were almost hunted to extinction by the whites.
Nevertheless, something extraordinary and inexplicable did occur around 12,000 years ago when modern man appeared out of nowhere, which science has been unable to thoroughly explain. It took primordeal man hundreds of thousands of years to develop their primitive skills. After the appearance of modern man, there was an explosion of innovations in a very short period of time, a few thousand years... Domestication of animals, agriculture, building dwellings, cities, all of which are described in the Genesis narrative, especially as it relates to the biblical story of Cain and Able, and their descendants.
So IMHO, there is no contradiction between science and religion.. it only exists where fundamentalist "interpretation" is concerned. In fact, the way I see it, science merely
confirms the Biblical account of creation. Which is exactly what I should expect to find.