The main advantage PostgreSQL has is additional data types that can be very helpful in some specific use cases, such as arrays (which are actual SQL standard, but unimplemented by the MySQL family) and geometric types (and a few other unique things). If the optimizations offered by these column types fit your use case, then PostgreSQL is probably the best choice for you.
If these sound like edge cases that don't apply to you - welcome to the club of 99.999% of RDBMS users. For that club, MySQL (or its MariaDB fork) are the best fit:
- High performance out of the box.
- Choice of a per-table database engine to optimize usage (need ACID compliance: InnoDB, need high read throughput: ISAM, need clustered in-memory access: NDB).
- True multi-master replication to increase write throughput in a cluster environment, as well as a variety of proxying technologies.
- Optimization for key/value and document storage use cases with the X protocol.
- Much simpler setup and maintenance.
In one company I worked for (granted, a few years back), we started with PostgreSQL and after failing to get any of the expected performance, purchased an EnterpriseDB (commercial PostgreSQL) license - and when the experts also failed to get us good performance, we moved to MySQL and I have never looked back.