Neanderthals had bigger brains than people today.
In any textbook on human evolution, you’ll find that fact, often accompanied by measurements of endocranial volume, the space inside a skull. On average, this value is about 1410 cm3 (~6 cups) for Neanderthals and 1350 cm3 (5.7 cups) for recent humans.
So does that quarter-cup of brain matter, matter? Were Neanderthals smarter than our kind?