It is most certainly not the amount of neurons that determine intelligence. Whales and elephants both have much larger brains with roughly twice as many neurons as we do. While it's true that species with a neuron volume below a certain threshold do not possess meaningful intelligence, that is not sufficient to claim that neuron volume is the main driving force of intelligence.
Aside from whatever difference in glial cells may exist (my knowledge of glial cells is abstract at best), it seems that unlike the rest of the body, it is primarily the cell structure, rather than the type of the neurons that determine function and efficiency. Presumably, because neuron functionality to a large degree revolves around growth and the mechanisms of neuron growth, the neuron's physical location relative to a connected neuron may impact functionality, as well as how the amount of neurons is distributed among the different centers (we have a much larger cerebral cortex than any other species, for instance). It is therefore from qualitatively and/or quantitatively superior brain centers that our intellectual superiority appears to arise, rather than from sheer neuron volume.