From what I have read they lived almost exclusively off meat...game. Many of the fossils turned up have "rodeo-like" injuries from hunting game with melee type weapons like spears and clubs. It seems to me that you have to be able to move well in order to catch these animals
I read that too, but I also read that their hunting habits involved being in the thick forest and basically catching the game off guard. If you literally had to spear an animal I would assume you would be in close contact with them. If you couldn't run very well I would assume you would get more injuries than if you could run.
A quick search yielded:
Researches including Karen L. Steudel of the University of Wisconsin have proposed that because Neanderthals had limbs that were shorter and stockier than modern humans, and because of anatomical differences in their limbs, it is theorized that the primary reason the Neanderthals were not able to survive is related to the fact that they could not run as fast as modern humans, and they would require 30% more energy than modern humans would for running or walking. [15] This would have given modern humans a huge advantage in battle. Other researchers, like Yoel Rak, from Tel-Aviv University, Israel have noted that the fossil records show that Neanderthals pelvises in comparison to modern human pelvises would have made it much harder for Neanderthals to absorb shock and to bounce off from one step to the next, giving modern humans another advantage over Neanderthals in running and walking ability.
I searched through the terms you gave me and all of them continually refer to the theory of interbreeding between Neanderthal and Homo Sapiens as an older theory and that it is of much debate now. The best link I found regarding the mtDNA is on talk origins (no surprise there)
http://www.talkorigins.org/faqs/homs/mtDNA.html