It's not just volume that counts but density (shorter paths make for more rapid signalling) — which is why misogynistic comments about women's brains being smaller are nonsense — they're smaller, but more densely packed (so, it at least evens out, if not making them, potentially, more capable than men).

That said, however, recent discoveries indicate that neanderthals were a lot brighter than they had previously been given credit for ... and recently it was determined that the earliest cave paintings yet known to exist were, in fact, not only probably by Homo Erectus but also included abstract, rather than merely represenational, elements.

So, yeah, they were a lot more advanced than people think but, if they also had a greater volumetric capacity then they might well have been a more advanced species wiped out by our intellectually inferior, brutiish ancestors.