http://www.expressindia.com/fe/daily/19970712/19355423.html
"He said his team ran four separate tests for authenticity - checking whether other amino acids had survived, making sure the DNA sequences they found did not exist in modern humans, making sure the DNA could be replicated in their own lab and then getting other labs to duplicate their results. Comparisons with the DNA of modern humans and of apes showed the Neanderthal was about halfway between a modern human and a chimpanzee."
Another recent article:
http://humanorigins.si.edu/evidence/genetics/ancient-dna-and-neanderthals
Reconstructions as per the image show the neanderthal having the same sort of rounded torso which apes have rather than the elongated human torso. The Neanderthal was an advanced ape.
An ape who used tools, played the flute, and wore clothing?
Current evidence indicates that Neanderthals were just another race of Man. Yes, there were anatomical differences, but nothing as radical as between different breeds of dogs.
Another recent article:Here's a reconstruction of what a Neanderthal would have looked like, based on the DNA evidence, using the article you referenced:
http://humanorigins.si.edu/evidence/genetics/ancient-dna-and-neanderthals
Looks more human than some of my coworkers.
The question is whether Neanderthals were a breed of homo sapiens, or whether they were a distinct human species.
Of course, your assertion that Neanderthals were "an advanced ape" is reasonable, since modern homo sapiens (i.e. "us") are also "an advanced ape".