Cofty: " Neanderthals had larger brain volumes than Homo sapiens."
Phizzy: "I remember reading that brain volume alone is not conclusive evidence for superior intelligence."
Although Neandertals had a larger cranium than Homo Sapiens that is not a sign of superior or even equal intelligence.
They actually had less of the frontal areas (where their skull slopes backwards) of the brain where fore planning originates. Also they had less cerebral cortex where general intelligence is to be found. Where they had more brain was to the rear of the skull in the occipital regions where vision is centered. Apparently he had more visual 'intelligence' than us.
That they were not as intelligent as us is shown by their tool making abilities and limitations. Their tools were more advanced than any other previous species but ours. We not only had a better tool kit, we had a tool kit that was improved throughout the duration of our species.
Neandertal on the other hand had a tool kit that stayed the same for 250,000 years without any advances throughout that time period. They also never made tools out of bone like Homo Sapiens did.
Another feature of Neandertals that would limit their knowledge was the fact that they seemed to have lived in groups of less than 25 members and were restricted to limited territories. Homo Sapiens traveled throughout larger territories in numbers approaching 100. The less people there are the less 'wisdom' there is to be passed down throughout the generations.