Earlier quoted context omitted.
That homo sapiens sapiens most likely displaced them, but that doesn't really mean as much as your comment might intend to insinuate. Neanderthals lasted half a million years, and the more we learn the more we appraise them as sophisticated. That said, they seem to have faced a caloric challenge in a world with sparse mega fauna. Based on everything I've read, modern humans pre-language excelled at one specific thing…
That's a pretty brutal selection mechanism. How fast and far can you go while slowly starving with your tribe in tow...
Maybe it's generally an advantage when it comes to exploration, e.g. finding new places to settle. Or maybe it's specifically an advantage when hunting, as in endurance hunting.