alt Hacker NewsMySQL was always behind in terms of features. In early 2000s it had very limited constraints. Most people were running in ISAM backend and did not even have transaction support. It was being used by people who did not understand how advanced relational DBs were being used. What changed is Postgres overtook its actual competition, which were Oracle, SQL Server and Sybase.
MySQL caught up as well as far as I know, but it still may have some poor defaults that are widely used.
In the early days, PostgreSQL was so much more awkward to deal with. Crash-prone at first, and then there was the whole business around having to drop the db during upgrades. It didn't really match MySQL operationally until around 2002.
During the dot com era it was common to develop and launch on MySQL with the intention of migrating to something else if they became successful (though your typical LAMP stack developer regarded Oracle and SQL Server as being deeply 'weird', so many were willing to stick with MySQL despite the well-known limitations of MyISAM).
From where I'm standing, it seems that PostgreSQL became clearly preferable for new projects from the mid 2000s onwards, but it was only the Oracle acquisition that began to push existing users off MySQL.