Neanderthals had ON AVERAGE larger brains than modern Homo sapiens populations. Important difference. Among modern humans the brain size varies quite a lot, without obvious consequences for those individuals' intelligence.
What this fact indicates though was that the Neanderthals were probably comparable to modern humans in intelligence, unless there is some major "software" difference we cannot sea. But the Neanderthal skulls indicate that despite their shape the key centres we associate with language and abstract thinking were comparably developed as ours.
Which, come think of it, is amazing - two human (sub)species have evolved towards full sentience independently, in different climates and very different circumstances. It would perhaps indicate that once the basic parts were in place, the evolution towards more brain power was unstoppable.
Yes, the Neanderthals' diet was predominantly meat, but that's more of an environmental response - there simply wasn't that much free stuff to gather as in the warmer climates. Large animals were plentiful and an excellent source of proteins, fats, and useful materials (bones, hides, sinew, etc.)
What's interesting is how practical archaeology changed our view of Neanderthal technology. Until relatively recently, it was assumed that since Homo sapiens tool set seems more 'miniaturized', it was better. But in reality, it was not - it was functionally equivalent to what the Neanderthals had.
The crucial advantage of Homo sapiens seems to lie in a different lifestyle, larger social groups, that sort of thing. This is very behaviour-dependent and unless we have a living Neanderthal to study, we probably will never know.
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