This is a very old thread but being a recent addition to this board almost every thread I find of interest is a very old one.
I had intended to study Anthropology at University and even bought the necessary textbooks, but when I went to sign up I found that they had pulled the course entirely due to supposed racism of the study materials. It was more a matter of phasing than anything else, they still used terms like "Sub races" back then, though this term was not what people thought it was. It was a classification denoting various population groups who had adapted to very different environments, such as Bushmen (Negrito), Oceanic Negroes, Pygmy, Maasai, etc.
Well that is not important to the question of the Neanderthal / Human connection, mainly since those were the pre DNA mapping days. Humans did not evolve from Neanderthal, both descended from earlier Hominids as separate branches. They were close enough to that root stock that in later generations they found they could interbreed.
The shape and size of the Neanderthal brain case suggests that they had a more active imagination and problem solving ability than early Humans, but they lacked advanced communication skills.
Interbreeding of Neanderthal and early Humans resulted in a vast improvement of the Human mind . Those Human hybrids now had more imagination and problem solving ability coupled with greater dexterity and ability to communicate complicated ideas.
I could go on but it would tread to close to subjects forbidden on this board.