One "quality of life" thing - you can wrap changes to the schema in a transaction, so that a given set of changes is atomic. (Elixir's Ecto and Ruby's ActiveRecord both have migrations that do this by default.) As far as I know, that doesn't work in MySQL.

There's also neat stuff like exclusion constraints: http://nathanmlong.com/2016/01/protect-your-data-with-postgr...

And there's the ability to do all kinds of neat geospatial queries with PostGIS - eg "list all properties within X distance from the curvy coastline".