I'll have to check my original source for that when I get home; I was under the impression it was because their forebrains were larger, but looking now I'm primarily finding claims that their whole brains were larger (which, given their larger body size, doesn't mean all that much).

This looks like the closest thing in the relevant wiki article to my claim:

The quality of tools found at archaeological sites is further said to suggest that Neanderthals were good at "expert" cognition, a form of observational learning and practice acquired through apprenticeship that relies heavily on long-term procedural memory.

but it's also tempered by things that might be evidence the other way. (Neanderthal tools changed little in thousands of years- is that because they found the local optimum early, or because they were bad at innovating?)

[edit] This argument wasn't in the book I thought it was in, so I'm slightly less confident in it. I think there's strong evidence that the primary differential between neanderthals and their successors was social, not mental processing speed / memory / etc., and will edit the grandparent to reflect that.