There are people with Neanderthal genes, so it cannot be true, that they all died out.
However it’s hypothesized that during the neolithic farmers immigrating from Anatolia/etc. lived alongside the hunter gatherer communities for quite a while. The types of environments preferred by hunter gatherers didn’t have the soil suitable for early agriculture.
But there probably was still quite a but of friction and violence. Also both groups were very different phenotypically, Western Europeans had very dark/black skin and often blue eyes while the middle eastern immigrants had pale skin and dark eyes.