I haven’t used Postgres, but it is one of the more popular ones recommended on the forums. I use MariaDB, which is a guaranteed drop-in replacement for MySQL. I highly recommend MariaDB over MySQL since they were acquired by Oracle, that is if you do not choose Postgres.
@pturmel is a big supporter of Postgres I think, and will probably have some technical reasoning.
Old post, but a little more insight
Postgresql Vs MySQL - Ignition - Inductive Automation Forum