I agree that Homo sapiens sapiens is a subspecies of Homo sapiens. I think that Neandertals were strictly speaking the same species as modern humans, meaning that they could have interbred to produce viable offspring. In fact at my college, I am convinced that some of the Neandertals on the football team were attempting this feat.

I had never thought of "Homo sapiens" meaning "self-aware" though. What an interesting thought.