The answer to the above-posited question: high-protein diets!
It was HOMO SAPIENS who developed farming, for the most part. Growing and consuming crops. The Neanderthal were carnivores. They hunted, killed, and consumed animal flesh. Miki Ben-Dor, a scientist at Israel’s Tel Aviv University, explains: “During harsh Ice Age winters, carbohydrates were scarce and fat was in limited supply. But large game, the typical prey of the Neanderthal, thrived. This situation triggered an evolutionary adaptation to a high-protein diet–an enlarged liver, expanded renal system [kidneys] and their corresponding morphological manifestations. All of these contributed to the Neanderthal evolutionary process…”
Neanderthals were considerably shorter than their HOMO SAPIENS cousins. (Claims that Bigfoot is nothing but a surviving Neanderthal fall flat on this point.) But it’s a safe bet they would’ve been far more powerful than them, or than US, since modern humans are HOMO SAPIENS. (Recent studies have found a little bit of Neanderthal in our DNA, though, so we know that some interbreeding occurred.) The consumption of meat is also a major factor in the evolution of HOMO SAPIENS, gifting modern humans with their bigger brains. Maybe this is why Neanderthals had bigger brains than we do. They simply ate more meat. They even sometimes ate each other. But then again, so do we. Maybe they did it more often?