The only 'evidence' for the latter view are claims by early 20th century cranks who never published any actual measurements. Ludicrous myths like that always seem to develop lives of their own in the English speaking world, seeing how there are thousands of books with claims about 7-foot-tall Cro-Magnons. Not sure why this is the case.
Coon addressed this already:
"FROM ABOUT 30,000 TO 10,000 YEARS AGO, the Upper Paleolithic Europeans lived in the lee of the ice from Spain to Russia. They buried their dead as the Neanderthals had done, and they wore fitted garments. From a grave below the permafrost at Sungir, about 142 miles(200 km) east-northeast of Moscow, a male skeleton dated at 22,000 years ago was disinterred in 1964. It showed traces of a fur shirt and trousars and bracelets and beads of mammoth tusk and the perforated canine teeth of arctic fox.
The Upper Paleolithic Europeans were modern Caucasoids. During their span of 20,000 years, their bodies changed physically very little if at all, for their adjustments to their environment left nothing to be desired. The famous "Old Man of Cro Magnon" was not a giant, as often depicted, but only 5 feet, 6 inches(168.4 cm) tall. The mean stature for twelve adult male skeletons was 5 feet, 8 inches 173 cm). The tallest 5 feet, 11 1/2 inchs(182cm), and the shortest was 5 feet, 3 inches(160cm). The five female skeletons recorded had a mean sature of 5 feet, 1 inch(155.5 cm) and a range from 5 feet, 1/2 inch(154 cm) to 5 feet, 2 inches(157.5 cm). This sex difference in stature varies closely with that in head size, as we shall presently see.
The limb bones of these people were rather slender, like those of Mount Carmel people, and their hands and feet were normal for slenderly built Europeans. We know this from negative silhouettes made by spraying pigment out of bone tubes over hands held against a cave wall, and from footprints found on cave floors.
There is little evidence that the Upper Paleolithic Europeans absorbed the Neanderthals that preceded them. Why the Neanderthals faded away is a mystery. One may postulate that they succumbed to diseases brought by their successors to which they had no genetic immunity, just as smallpox and tuberculosis decimated the American Indians; or one can suppose that they were hunted down by the invaders(which has also been done in modern times); or perhaps they died of crowding or of grief. (Is it possible that, because of phonemic limitations, they could not learn their invaders' languages? Or only with a poor accent?)"