Actually, Neanderthals has bigger brains than us. And they were slightly shorter. And their musculature was much denser than ours, which means they were much stronger, which means they were adapted for hunting, which means they probably moved incredibly quickly. Like someone mentioned above, they were better than humans at essentially everything. That’s why humans exterminated them. And it’s happening again.
There are other explanations besides your genocide theory. Probably what happened is they were out bred and absorbed into the larger Homo sapien population.
“they were better than humans at essentially everything.”
Except thinking (probably) and talking (maybe).
Except surviving....
Well, you've proved your case.
: )