I propose a hypothesis, summed up by changing our name from Homo sapiens, "wise man" to Homo mimicus, "mimicking man". Many animals mimic each other's behaviour but we do it more often and with greater fidelity. Our compulsive copying encodes collective knowledge into our society, and it is really our society that possesses humanity's "intelligence".
Consider two islands, identical except that one has a population of highly intelligent but vain apes, while the has a population of gregarious dimwits that love mimicking each others' actions.
The "sapiens" are always inventing marvellous gadgets but their vanity is such that they will never us another's clever idea.
It is only by accident that a dimwit discovers that poking a honey-coated stick into a hollow log will pull out some delicious termites. But, seeing this many mimicus copy it. Some of the copied actions improve the chances of survival of the sub-population performing them.
Which species is most likely to develop megacities or rocket ships? I'd back the dimwits.