Brainsize does not matter.
There are people with very large brains that are stupid, and people with far below average brainsizes that are geniuses.
In fact, although there is a positive correlation between brainsize and intelligence in modern humans, it is a very small one.
Quality is more important than quantity.
I think the neanderthals where civilised enough to hava culture, but to claim they are more 'neurologically advanced' is ridiculous. There is no evidence for it.
I'm not saying that I make the argument....I was just explaining the other poster's position.