So far it is looking like the number of neurons in the cerebral cortex is the best indicator of intelligence.

http://mitp.nautil.us/feature/227/the-paradox-of-the-elephan...

We started as basic primates, started cooking our food, getting more nutrition, allowing our guts to shrink, allowing us to spend more energy on our brains, growing more and more neurons in the important bits, at which point things spiraled away using our new language and technology to make better technology.

(Not a real biologist)