Postgres is widely acknowledged as the leading open source database. It's frustrating that it remains a second class citizen on AWS.
Postgres is still comparatively new to AWS, whereas MySQL was one of the first (the first?) supported RDS engines way back in 2008/9 or thereabouts. I guess this is due in part to the relative latecoming of built-in streaming replication support in Postgres, it's only been since 9.0 that it's been a thing, and 9.1 that it's been production-ready, which coincides with it's rise in popularity over recent years (well, that and Oracle buying Sun..).
My money is on support for x-region replication being announced late this year; it's a feature I'm interested in for sure.
I know, from personal experience that most large companies are using mysql, even if they use postgresql they're also using mysql for smaller things..
to give some examples the only company I ever worked in which used pgsql as a direct backing store and primary database still used mysql to manage it's internal documentation servers and caching systems (records used to keep track of what is cached inside of memcached).
simply due to the ubiquity of the tools developed around mysql and the notion that you will never have a hard time finding a person with mysql experience causes people to choose mysql when designing new things.
currently I'm getting a lot of force against postgresql adoption in my company, even though it makes complete sense for my project- the fact that "nobody understands it" and that "tooling exists behind mysql" is enough to keep the status-quo for a long time unless someone fights really hard (which I'm doing).
Plus it's all hooked into the rest of the AWS system, which can be really helpful.
I think RDS is great until the needs are extreme enough to require a full-time sysadmin or DBA. Nowadays, though, that means you're dealing with quite a lot of traffic (or just an edge case in terms of your read/write ratios or latency requirements).