Homo Neanderthalensis*, better known as the Neanderthal, has lived together with Homo Sapiens, the modern man, namely us. I've heard that the Neanderthal were found to be living at the bottom of valleys, right next to the river. Modern man was found to be living on the slopes a bit higher up. At first glance it would seem the Neanderthal had the better spot, yet by living on the slopes modern man had an advantage. In this era, man was already a hunter, and they largely lived with the flow of the animals. They were settled as in they probably had a winter location and one for summer (either further southward or to the north, obviously). Farming hadn't been invented yet.

So the large herds were the main source of food for both the Neanderthal and Homo Sapiens. I said modern man had an advantage by chosing the slopes. Ofcourse, they're less effected by floods, but far more importantly, they could see the movements of the great herds. They would see either the movements or the dust cloud way sooner than their Neanderthal collegeas. Also from high above, you can plan better, as you have a broader overview.

Now an interesting question is, did modern man survive because they chose, maybe by chance, the slopes while the Neanderthal chose the valley? Or, was it a deliberate choice, which would indicate higher intelligence, compared to the Neanderthal. Apparently it was the latter. Neanderthals had a physique making them stronger and probably of a tougher constitution. But, there wasn't a lot of room for a really big brain, because of their big boned and strong heads. So they likely really weren't too bright.

In comparison, Homo Sapiens is rather frail. But they do have room for a bigger brain. Early Homo Sapiens likely was very ignorant to the ways of the world, but born with inherent intelligence and curiosity. Where the Neanderthal would be conservative and slow to change, Homo Sapience looked into everything he saw and either adapted their way of life to it, or even shaped it to their wishes and benefit.

As Darwin put it so correctly, survival is about being adaptive to change. Over (and under) specialization leads to decline and finally extinction. The Neanderthal was stuck in their primitive habits and were soon left behind, compared to Homo Sapiens. While Homo Sapiens flourished and grew, the Neanderthal fell back and became far less numerous until they finally died out. I don't know** if Neanderthal and Homo Sapiens were able to have sexual relations. Perhaps if they were, they blended in with Homo Sapiens in a limited way, leaving a part of their heritage in all of us. If not, they just died out.

* yes I looked that up :P, fyi, the name comes from 'Neander Thal', which means Neander Valley.
** perhaps no one does, I have no idea if that has been investigated or not