IIRC Neanderthals generally were both built physically stronger than "modern humans" and had bigger brain capacities too, though they are assumed to
have been stupider than people today (nothing to do with education and technology, but the ability to figure things out like any other human would).
If anything I would think they should have been the ones to survive and we might have gained something if there was interbreeding.
I've always been fascinated with ancient humans. Imagine there really was a time with large monstrous predators and different races of people. Is
like a fantasy novel!!!
Shamans, Medicine Men, varied religions and beliefs, Terror Birds, Magalania, Short Faced Bears, Sabre Toothed Big Cats, Dire Wolves!!!!