Interestingly, if you use 23andMe's genetic analysis service, it'll tell you how much Neanderthal DNA you have. The average European has 2.7% (I have 3.2%).
In the article only the negative effects of Neanderthal genes are discussed. Is this because genetic datasets are mostly about gene/diseases correlations, or is it because the researchers did not analyze any gene/benefits datasets?
The third option (all Neanderthal genes are bad) does not seem reasonable.
I like the idea that Neanderthal genes helped Homo Sapiens spread, through increased resistance to diseases unique to Europe. Explains why their gene contribution is so prevalent - it directly contributed to survival in the new environment.