“Superior to” in a moral sense?
Cowboy Bob is right. No, not in a moral sense, but in a pragmatic one. Neanderthals were smarter than humans — not only did they have bigger brains, but they left behind better technology (for example, they made flaked spear heads out of obsidian; those things are so sharp you can shave with them). They were much stronger than humans, and had much better night vision — their eyes were easily 50% larger than ours and spaced farther apart. In fact, the area of the brain that was most noticeably larger was the occipital lobe, which controls spatiotemporal perception. So, you have a hominid with the best spears in the world, musculature to throw them farther than anyone else, with pinpoint precision, on a moonless night. Oh, and they lived in glacier-covered Ice Age Europe, which humans couldn’t last a day in without freezing to death.
So, yes. Superior.
The theory is that humans exterminated them through simple persistence and sheer numbers. The changing climate helped the humans too, to an extent.
It’s also possible that the Neanderthals adopted a religion that considered it blasphemous to fight back against the humans, even as the humans were killing them. Sounds familiar.