I had tested running moodle with MySQL and PostgreSQL and I got very big different in performance.
I got no problem with both database, when my moodle site hitted by no more than 15 users. The problem started when we got more than 20 users online at the same time. My moodle site that used MySQL database hang up, even the CPU usages under 40% and Memory Usage under 50%. But when i run with PostgreSQL, i got no problem even my moodle site hitted by more than 300 users.
In my experiences, running moodle with MySQL database, need higher Hardware specification than run it with PostgreSQL.