Community is king
The most striking difference between PostgreSQL and MySQL may not be technical at all. Open-source projects are, by definition, all about the community. The community of developers that create and contribute to open-source projects make them come to life. Essentially, there are two different kinds of open-source communities.
First, there are pure open-source database projects that are organized around independent and self-funding communities. PostgreSQL is the oldest and largest independent open-source database community of this kind. The benefit of such a community is true vendor independence.
On the other hand, the second kind of open-source community may have a vendor that controls the project and the project could potentially be "purchased." MySQL is one such example. The MySQL project was initially funded and controlled by MySQL AB, a commercial company that employed all the key developers and architects of MySQL. The MySQL community has more recently been controlled by Sun and now Oracle.