The first Neanderthal found in Germany in the Nineteenth Century turned
out to be an older man who had serious arthritis, which left him hunched
over.

This along with the "beetle brow" ridges over their eyes contributed to
the image of the Neanderthal as the stereotypical hulking, hairy, and
none-too-bright brute.

Maybe some of their kind were, but it's probably unfair to categorize all
of them that way. It was shown in back in 1975 that they walked the
same way we do. They had physically larger brains than Homo sapiens,
they did have some forms of art (including the discovery of a flute-like
instrument), they made tools, and they had rituals for burying their dead.
Plus they survived on Earth for about 200,000 years without once needing
a cell phone.

As for physical strength, one archaeologist did describe how an adult
male member of their species could have plowed through an NFL team
with ease.

For some fun speculation on how things might have gone had the
Neanderthals become the dominant primate species on Earth, see
Robert J. Sawyer's SF novel Hominids.

http://www.sfwriter.com/exho.htm