Wow, the difference between the US and the rest of the world is very stark.
I suspect it largely comes down to a combination of (1) price related issues and (2) completeness of Apple's ecosystem in the US.
Regarding the first, the issue is that in the US, the perceived difference in price between Android phones and iPhones isn't as large, since the carriers absorb a big chunk of the difference. Internationally, end-users feel the full difference in phone prices.
Regarding the second, Apple's whole "ecosystem" is just a lot better developed in the US (completeness of the iTunes and App stores, and just as importantly, the pervasiveness of the retail stores).
If Apple can get out lower cost iPhone models internationally and build up the ecosystem, then perhaps Apple can replicate their success in the US globally.
Some of the "smart phones" in parts of the world are barely more than a "feature phone," running an early version of Android. Those users have little need for an ecosystem. It's not to say that many of these present users will never become an iPhone user, but, for now their simple needs are being met.