I think Neanderthanls may have smarter than homo sapiens; although, they had smaller frontal lobes relative to the rest of their brain size. Their overall brain size was bigger. Their childhood development was also slower than human. This is associated with increased intelligence. As far as tool use and signs of intelligence, their tools seemed similar at similar points in history. Much of human intelligence was fine-tuned late in human evolution.
Humans were faster and better hunters so could handle a wider range of game. This may have been one of the reasons why humans overtook Neanderthals.