Is it possible or has a dna comparison been done between Neanderthals and modern humans?
Yup. They say there's no connection. But, I don't believe it. (Yet)
No. Nope. Never. There has been no such DNA comparison.
There was a (so-called) study of some mitochondrial DNA (iow, not DNA from the cell nucleus, the kind that gives us hair color and everything else) said to be from a sample Homo Heidelbergensis (believed to have been a forerunner of the Neandertal) and not, say, from bacteria which reproduced like wild as it munched the then-recently deceased bones.
The comparison was of fewer than 400 base pairs, out of a presumed original 16,000+ base pairs such as are found in the mtDNA of living humans.
So, the study was bogus -- a tiny sample of broken DNA bits, patched in wherever the researchers pleased. The conclusions fit the original assumptions, and the Replacement advocates were happy with that.
In addition, even if one accepts the assumptions of mtDNA studies, there's no reason to believe that living matches for the 387 (or whatever the number was) base pairs could not be found.