Postgres was developed over a long period of time with careful attention to architecture, robustness, and extensibility. It also focused on both external and internal documentation and cleanliness. And, it followed the traditional database system model with a cost-based optimizer and everything else.
As a result, we see a very robust developer community. It's a real machine -- churning out high quality releases every year with a great mix of newsworthy features. Enterprises and startups alike are flocking to postgres for a huge variety of use cases.
Slow and steady wins the race (and it doesn't hurt to be 5 tons and have tusks) and isn't tired afterward. And in databases, it's good to play for the long term because that's how long the data will last.
I wouldn't trade that for some first-to-market popularity.
An undeniably, there is a shift happening, even in parts of the market that were a MySQL stronghold. Heroku and their customers use postgres for multi-tenancy. Instagram uses postgres for photo-sharing.
I think MySQL has been very complacent because they are the default for a lot of simple web apps, and that keeps their numbers high. They aren't really breaking into new markets -- postgres is winning the geospatial market big time, and is always coming out with new features to break into new markets (personally, I am trying to advance postgres into the temporal database space).
MySQL cluster is highly popular in telecom. http://www.mysql.com/customers/industry/?id=78