In no way were they nearly as smart as we...their frontal lobes were much smaller.
My response was to a poster who said that we could beat Neanderthals at chess. Actually, Neanderthal brains were larger in the occipital and parietal areas, those areas directly involved with spatial orientation. Larger frontal lobes have little bearing on winning at chess.
http://www.chesscircle.net/forums/showthread.php?410-article-chess-and-the-brain