An interesting hypothesis about Neanderthal brain size is that most of their behavior, including tool making, was hard wired in neurons rather than learned through intelligence and culture. Neanderthal tools and dwellings are identical across tens of thousands of years. Human tools vary a lot from culture to culture and across time even if function is unchanged, because of imperfect propagation across generations.

The idea is that the extra gray matter in a cloned Neanderthal's head would have him instinctively finding good stones to shape into tools in a specific way, even if nobody ever showed him how to do that.