Till about yesterday, MySQL was little more than a CSV file on wheels, and even current popularity is mostly driven by two decades of LAMP.

You can be sure that PostgreSQL will be applicable for any work load that MySQL can handle, but not necessarily the other way round, so if you actually have the freedom to make a choice, go with PostgreSQL.

In particular, because PostgreSQL has a lot more features, people imply that the other one, for the lack of those features and its associated complexity, must automatically be faster. Which isn't true, neither generally, nor in special cases, since the latter one can go either way - your particular query might just run 4x on PostgreSQL. There is also no universal approach to even benchmark performance, since every database and query will have completely different characteristics.