Probably the opposite of that- it seems likely that neanderthals were physically stronger, and may have even been smarter as well but we killed them off because we had more of the type of traits you're stereotyping them with: humans band together in large groups and systematically eliminate our competition through organized war/violence, politics, etc.
I think it's pretty ironic that humans have formed a cultural idea of us being superior to Neanderthals based on stereotyping them as having traits that are actually more characteristic of us.
"Projections change the world into the replica of one's own unknown face." -Carl Jung