By greater do you mean greater than those of H. sapiens who lived at the same time? AFAICS, the Wikipedia articles seem to state the opposite: that Neanderthals, late ones at least, were technologically and culturally inferior to H. sapiens of the same time.

The paragraph right after the one you quoted from your second link states:

There once was a time when both human types shared essentially the same Mousterian tool kit and neither human type had a definite competitive advantage, as evidenced by the shifting Homo sapiens/Neanderthal borderland in the Middle East. But finally Homo sapiens started to attain behavioural or cultural adaptations that allowed "moderns" an advantage.

The following paragraphs (through to the end of that section of the article) detail tools and cultural or social innovations that were (by conjecture) exclusive to H. sapiens. There are no specific things listed that were exclusive to Neanderthals. What "greater achievements" do you refer to?

Also, I see no basis (at least in the WP article) for "the obvious fact that Neanderthals were highly intelligent", except for brain size which is hardly conclusive. Why can't we conclude that they were considerably less intelligent than their contemporary H. sapiens?