Researchers at the Max Planck Institute for Evolutionary Biology in Leipzig, Germany, plan to reconstruct the genome of Neanderthals, the archaic human species that occupied Europe from 300,000 years ago until 30,000 years ago until being displaced by modern humans.
The genome will initially be reconstructed using DNA extracted from Neanderthal bones that are 45,000 years old, which were found in Croatia, though bones from other sites may be analyzed later.
As far as I'm aware, they're talking about nuclear DNA, not mitochondrial DNA. To completely and fully understand the difference between Humans and neanderthals (or to use a more scientific and neutral terminology, Homo sapiens and Homo neanderthalensis), we need both, especially to find out if any interbreeding ever occurred. But this analysis alone should tell us a good bit about exactly how similar neanderthals were to sapiens. There are several important questions we don't have the answers to yet, like their brain size and whether they were capable of speech yet. Actually, we know next to nothing about their cognitive abilities, although we think that they had similar sensory capabilities to ours. They did have bigger noses, mouths, and eyes, so it's possible they had more brainpower dedicated to those areas. However, their material culture remained at a primitive state for their entire existence, whereas sapiens quickly surpassed them in technological advancement. But their brain case was actually larger, so it's all up in the air.
Theoretically, at some day in the future, a complete DNA reconstruction would enable us to create a cloned neanderthal so that we could get these answers definitively. That's a moral and ethical nightmare, so I'm not even going to think about that. As to what we hope to learn from just the sequencing alone, finding out whether they had language is the big one.
Dr. Paabo believes that genetic analysis is the best hope of doing so. He has paid particular attention to a gene known as FOXP2, which from its mutated forms in people seems to be involved in several advanced aspects of language. The human version of the gene differs at two sites from the chimp version. Knowing whether the sequence of the Neanderthal gene is closer to chimps or humans would help decide whether they had advanced speech like people or some lesser form of communication, perhaps without syntax.