In primates brain size does determine intelligence, because of a difference in primate brains from other vertebrate brains. Other vertebrates have larger brain cells the larger their brains are. Whales have the largest brain cells of any vertebrate. More importantly than the size of brain cells, however, is the types of brain cells, their organization, and how they are used. It should be easy to grasp that what we call intelligence involves understanding how to manipulate stuff with hands, and that whales don't specialize in the same kind of intelligence.
But primates, and people are primates, have more brain cells the larger their brains are. Even though our brains are much smaller than whales, we have more neurons per kilo of body mass than whales. The larger a primate brain is, the smarter the primate is. Cro Magnons were far smarter than modern man, and Neanderthals made them look stupid.
War is not won by intelligence, but by brute force (exceptions exist, but aren't the rule). Neanderthals did not live in social groups, as H. sapiens do. A village of smaller, weaker, dumber Cro Magnons might defeat a family group of Neanderthals, who would have one or two adult males to defend them. We simply zerg rushed them, if conflict occurred. We probably mostly didn't, because they probably mostly won when it happened.
It is likely we did not bother (or dare) to kill them personally, because Cro Magnons and Neanderthals co-existed for tens of thousands of years. We probably just took over their territory, and made it impossible for them to survive on our leavings.
Neanderthals must have been incredible warriors. I am confident one Neanderthal would have been happy to tackle ten Cro Magnons without much fear of losing. Neanderthals took down mammoths, wooly rhino, and similar multiton prey alone, or as a family group. They weren't long distance runners, and their immense strength was all for short bursts, like sprinters compared to marathon runners. Their reaction times were probably much quicker than ours, like birds. In battle one would have danced circles around whole tribes of weak, slow, stupid sapiens.
They had no villages, no huts. They were completely integrated into the ecology, and didn't alter it at all. It's very difficult to grasp how such a natural mode of living is extremely demanding of intelligence, until you've tried to live off the land, but I have done so, and would probably die in a few months if I tried to do it today. You need to know every life stage of every plant and animal necessary to your living, and travel long routes, along which you also need to know every shelter, source of salt, stone, and etc. It's necessary to master all trades, not just to specialize in scratching lines in the dirt where you plant some seeds.
You need to know when and how to do all that, and do it in a landscape full of lions, tigers, bears - and the most deadly of predators, feral packs of men - with nothing but a pointy stick to protect your women and children. Neanderthals did that for ~50kyr after H. sapiens showed up. They were hella smart.
We, and our forefathers, hunted such game in packs, and we didn't jump on them and stab them to death. We dug pits they fell in, or drove them over cliffs by setting fire to the steppe. I don't think any H. sapiens could have tackled a mammoth bull alone, and I think Neanderthals lived by doing so routinely. As warriors, we were no competition at all. Only as we dominated the whole landscape with our eusocial tribes were we any challenge to Neanderthals.
Personally I don't think Neanderthals went extinct in the way we think of mammoths or wooly rhinos going down. I think they were absorbed into Cro Magnon tribes until their genes were simply mixed in, and they ceased to exist as distinct people. That's where the food was, and Neanderthals were far smarter than us, so that's where they went.
I think Neanderthals were the Nephilim of legend, giants among men in terms of strength and intelligence, although on average shorter than H. sapiens (this may more apply to H. denisova, who apparently averaged ~7 foot tall. They really were giants among men, and probably were absorbed the same way as were Neanderthals). I think the Norse trolls also refer to Neanderthals, and Beowulf may be a dim recounting of murdering the last hold out that refused to integrate into human society. I find it interesting the story of Beowulf and Grendel also alludes to Grendel breeding with human women - probably why they had to kill him.
What mere man could compete?
Your claims are interesting!
However, it was recorded in the Bible that humans fought and destroyed the Nephilim. The Jews initially lag behind the development of civilization over Egypt, Babylon, Greece, Rome, and Islam, but eventually won the final victory through Christianity.
At first, the Neanderthals may have had superior intelligence and power over humanity. However, the evolution and development of mankind conquered the Neanderthals.
No. Where are our conqered slaves? We conquered nothing and no one with our development - except ourselves. We are being domesticated, enslaved today. Look at the pallets of bricks American cops are leaving for protesters to throw at them.
What does that even mean?
It means we are not smart, we are not developed, and we are their property. It means collectivism is slavery.
It means those of us, those remnants of Neanderthal genes that yet live today, are the only free men there are. I may not tackle a bull mammoth with a pointy stick alone for my dinner, but I will not enter the corral and enable my oppression by throwing bricks they supplied at them.
I always return to decentralization, the individual possession of means of production, as the solution to problems, and the means of creating benefits. Who better than Neanderthals to model independent means?
Neanderthals, my friend, will win this contest, not H. domesticus, not the domesticated cattle of banksters, but the lunatic fringe that isn't part of the compliant herd.
Thank God I am such a lunatic =)
Edit: >"...power over humanity..."
I do not see that Neanderthals ever exercised any power over humanity, not once in the ~50kyr we invaded their territory. What I see is that they have become the power of humanity, the very model of what we today must undertake to be free and human, when the enemy of humanity seeks to make mandatory injections of DNA altering 'vaccines' that will actually and literally turn us into GMOs, it is that refusal to enter into society, to enter the corral where the herd is, to remain reliant upon ourselves alone, that will retain our humanity.
It is the Neanderthals that will save humanity.
In Korea and Japan, Neanderthals are degraded as inferior human beings who have failed to adapt to environmental changes.
So, your claim is shoking! hahaha
Many people never suspend their beliefs and closely examine them. We absorb our culture, our foundation, and base our every thought on unexamined artifacts of our upbringing without ever choosing it.
Carefully examining the tens of thousands of years Neanderthals weren't extinguished reveals their sublime competence to survive. They were smarter than us by far. Today, particularly in places that are densely populated and have been for generations, being a faithful member of society is far more beneficial than being smart.
We needed to be social far more than we needed to be intelligent.
I understand!
Seek first wisdom. You are on the right path.