We know they had a larger brain volume than us, even when correcting for overall body size. That much is an established fact. What that means, if anything, regarding their behavior & abilities is strictly, and highly, speculative.

(Still lots of fun to think about. If I were to hazard a guess, it would be something along the lines of greater neoteny in h. Sapiens sapiens. For an analogy, compare dogs and wolves. Wolves have larger brains, but dogs have a greater ability to read social cues.)