Now since both the neanderthal and the cro magnon were eventually living during an ice age evolution had to give them a body size that would help them survive. The cro magnon were built strong and tall (average size being 5 feet 9 inches) while the neanderthal were short and stocky but strong. This stockiness was a benefit for the neanderthal because that meant they were able to keep more body heat than the cro magnon. However their bodies along with life style would be the start to their down fall.
When the climate changed a lot of the food supply was scarce, and most of the neanderthal diet consisted of deer, wild boar, and the occasional mammoth. But just hunting was a very dangerous activity for them. Reason being they charged at their prey. If they lost the kill they would starve until another opportunity arrived or some would be killed by the animal they were after. In times of extreme hunger they would eat the weakest of their own for the greater good of that individual tribe. With this climate change though, the cro magnon thrived. They, unlike the neanderthal, would not charge at their prey, instead they had taught themselves to make spears that when thrown would impale the animal. Also, through that they had wonderful hand/eye coordination and began to fish.
Even though it was an ice age the temperatures fluctuated frequently. For this the cro magnon could adapt, sadly though, the neanderthal could not. Once the neanderthal became accustomed to a certain life style the climate change would be so drastic that the life they had worked so hard to get used to was gone and replaced by completely different animals and plants.
With two types of hominids living in the same place at the same time for 10,000 years, they were bound to cross paths. We don't know what happened when this did happen. There have been theories that the neanderthal would spy on these new creatures and try to apply what they were seeing to their life, or that the cro magnon killed them off. But current studies have shown that there was a meeting of the minds because of artifacts found amoung the cro magnon and amoung the neanderthal of which the neanderthal hadn't the technology or knowledge to make. There also have been theories with DNA proof the neanderthal might have just interbred with the cro magnon. So the neanderthal might not be extinct, we all might have a little neanderthal in us.