Following The Rational Optimist by Matt Ridley and many other sources, I suspect the dominating differences between chimps and us is abilities we have evolved that greatly enhance the effectiveness of our working together in large groups. The more you enable cooperation, the more things like complex language and cognition suitable for highly specialized (i.e. a specialized cog in a larger machine) production.
It seems to me that introspection is valuable even in a non-cooperative world: if I can fine tune my reactions to prey and my attractiveness to the opposite sex, that is valuable in a band of 20 possibly nearly as much as it is valuable in a band of 20,000.
I love watching the "naturalness" with which female humans game the attractiveness-system. While at a young age I don't think their instrospectiveness extends to them realizing they are gaming a system, I do think that they spend a lot of time studying themselves and figuring out how to enhance their attractiveness with increasingly well developed skills and clever fashion decisions. Is there anything like this "self-enhancement" in an individually customized (introspective) way among other primates or other animals?
The Francis Crick Memorial Conference, held in Cambridge last month, has come up with the Cambridge Declaration on Consciousness (PDF).
tl;dr humans still aren't special, consciousness seems to arise in quite a variety of nervous systems and working out what it is is a problem in neurology.
We declare the following: “The absence of a neocortex does not appear to preclude an organism from
experiencing affective states. Convergent evidence indicates that non-human animals have the
neuroanatomical, neurochemical, and neurophysiological substrates of conscious states along with
the capacity to exhibit intentional behaviors. Consequently, the weight of evidence indicates that
humans are not unique in possessing the neurological substrates that generate consciousness. Non-
human animals, including all mammals and birds, and many other creatures, including octopuses, also
possess these neurological substrates.”