Cranial capacities of Neanderthals were larger than those of modern humans. Of course Neanderthals were not as technologically advanced as we are, but the argument can be made that they were neurologically advanced than we. There is more to intelligence than tool-making ability.
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.