So the Neanderthal story is that that sub-species left Africa 100s of 1000s of years ago. Strains spread all over ME, Europe and Asia, but not back into Africa.
50,000 years ago, the African modern human subspecies followed, meeting Neanderthals in the Middle East and Southern Europe. Some inter-breeding occurred, extensive enough that the average European has 1.5 – 4.0% Neanderthal genes.
From the differences between current Europeans and the current Africans, we can infer Neanderthal characteristics.
Obviously Neanderthals had tiny dicks.