Since its initial discovery in Germany's Neander Valley in 1848, Homo neandertalensis, the Neandertal, had undergone quite a dubious reputation. From sensationalist beginnings as big, hairy apes, they had, for the longest time, become the stereotypical caveman--big-boned, brutish and all-out primitive.
But in recent years, the image had undergone a renaissance. We have found evidence pointing out possibilities of omnivory (evidence of chewing medicinal plants), arbitration (art used for purposes that aren't necessarily practical) and even display construction (The Astonishing Age of a Neandertal Cave in France).
So culturally, technologically and dietarily, Neandertals were no different from us. So why did they vanish 30,000 years ago?
We can't say with 100% certainty. The most traditional assumption is that their brutish appearance, actually a necessity to deal with the hostile, frigid environment of Ice Age Europe, made them too specialized to deal with change. Maybe it was our sexual joie de vivre that bred them into extinction, absorbing their genes into ours. (Which would make sense, considering that 1-4% of Eurasia's genetic population was found to come from Neandertals.)
But perhaps the most overlooked reason may be that they never expanded their social structures beyond clans (small groups tied together by descent.) Their particularly small population densities meant that they could not expand their numbers to the extent that tribes do.
But let's say they do.
In this alternate scenario, Neandertals ruled Europe in a higher population density, numerically, culturally and technologically akin to Native American or African tribes. When Homo sapiens made their first steps to Europe to cross paths with Neandertal towns or villages, would this change the course of genetic admixture between species in any way?