Contrary to pop media, there is also literally no clear evidence they even engaged in the most basic of symbolic behavior such as self adornment or even primitive art. [1] Now mostly disregarded efforts to show such were highly optimistic. This included things like bird bones being laid near a corpse = self adornment, or scratches on a cave floor = art. Even in what they did do - hunt, despite engaging in hunting for hundreds of thousands of years there are extremely high rates of traumatic injury among neanderthal corpses which suggests they never even managed to refine their hunting ability.
And the brain size : intelligence correlation is just so broken in so many ways. If you go based on raw size sperm whales should be, by far, the most intelligent species there is. If you go based on the ratio of brain matter to mass, ants should be, again by far, the most intelligent species there is. Suffice to say you're probably not too worried about being put in zoos by sperm whales or ants.