No evidence for cognitive inferiority of any kind.
Now all they need to do is admit those ridiculous reconstructions of their faces and bodies are even farther off the mark and they have almost caught up to our wake. They admit as much here, conceding that their appearance was never more than a theory based on some very badly assembled skulls which have never been made public for peer review. They left out most of the important information, including that the first Neanderthal ever found was a 90 year old man who had rickets so severe it warped the entire shape of his body including his skull. This man had apparently lived his entire life underground. Neglecting to mention this to visitors to the British Natural History museum who saw that skeleton in the front hall for the past 150 years is nothing less than scientific fraud.
When they say Neanderthal are they speaking of Mousterians, Amud or Denisovians? The last two looked like modern people. The Mousterians were no more different than is common in slavic countries. All that Fred Flintstone garbage is pure make-believe and inventive fantasy.
If they had told people from the beginning that Neanderthals towered at 6'2 on average in the south, how would they have ever fit him onto that "Ascent of Man" pictorial chart they loved so much? If you depicted Neanderthal correctly, he would have been taller than modern people, more muscular and with a bigger brain case in addition to being more genetically symmetrical in his face and entire body. How is that Neo-Darwinism working out for you, Saps?