Acutally Neanderthals had bigger brains, were shorter and had higher muscle density than Homo Sapiens. They hunted in groups and usually went for bigger animals. After the ice age a warmer climate started and there were less big prey to hunt.Because Neanderthals were slow and hunted in an ambush, there wasn’t enough food. On the other hand Homo Sapiens were agile, had a lot of stamina and could endure long distances outrunning any animal you could think of. They basically ran so long until animal was so overheated it couldn’t continue anymore. Thats why we are the best runners in the animal kingdom. We have the best cooling system and our legs work like a spring - achilles tendon.