I believe it would be a good bet that another human species living alongside us would have merged with us by know.
Personally, I think that the most likely explanation is that most mixing came through adoption of fertile women into the human tribes. Males of other tribes would probably not have been accepted so readily, and likely driven off or killed, but fertile females would have been more easily integrated. From there, you naturally get a mix of the two.
The relative percentages of Neanderthal and Sapien DNA in modern humans would indicate that Sapiens outcompeted the Neanderthals and relatively few interbred with us.
Neanderthal mtDNA is fairly rare in humans while nuclear DNA is much more common. Oddly enough in population with higher percentage of nuclear DNA mtDNA is rarer so it’s not clear which side did the gene transferring.
It could be that there are other reasons behind this for example that Neanderthals and modern human female offsprings were less likely to survive or reproduce than males.
But overall it’s really not clear how the populations mixed and who did more of the pillaging and raping.
When two different dog breeds have pups those mutts are just as fertile as any other dog. When a horse and a donkey have a mule that mule is almost entirely infertile. The first human/neanderthal descendants were probably significantly less fertile than their parents but generations of selective pressure seem to have purged the particular genes that were causing problems which you would expect to include mDNA.
Reproduction through “love” is a fairly modern concept, while not all rape was at the hands of an invading army or by some serial predator in a dimly lit cave (or parking lot) the sexual dynamics were very different across the population and would be considered rape by most people today especially in the west.
I roll my eyes at people who talk about American "rape culture". But we definitely are a rape species!