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Steve Hsu once estimated that if we cloned Neanderthals and raised them in modern times, they would average IQs of 70.  Not sure how he arrived at that estimate, though he does mention their genetic affinity to humans.

I’d estimate a much higher figure:

It’s been reported that the genomes of humans and chimps are 98.8% similar, humans and Neanderthals are 99.84% similar, and that different human races are 99.9% similar.

On an IQ scale where white Americans average 100 with a standard deviation of 15, chimps score around 14.  Thus a 1.2% genomic gap may have caused a 86 point IQ difference.  Assuming a linear relationship between genomic gaps and IQ gaps and independent genomic effects, we might expect that (controlling for environment) white Americans and Neanderthals to differ by 11 IQ points and white Americans and other races to differ (on average) by 7 IQ points?

Thus if we cloned Neanderthals, raised them in average white U.S. homes, we might expect them to score 89 on IQ tests normed on U.S. whites (25th percentile of the U.S. white distribution)

Many Neanderthals might end up in jail since 90 has long been the average IQ of U.S. criminals, and the Neanderthal’s incredibly muscular build (enhanced by modern steroids) might give them the confidence and roid rage to engage in violent crime.