In my past life as a geospatial DBA, I had to navigate users and managers who belonged to different database teams (PostgreSQL, MySQL, SQL Server, Oracle, etc). When I was lucky enough to work in a shop that supported open source solutions, I was often asked by members of team MySQL, “Why should we use PostgreSQL as our geospatial database when MySQL has spatial data types?”
The answer: PostGIS.
Sure, MySQL has the ability to run spatial analysis (with some prodding). But PostgreSQL + PostGIS wins in:
So if you like to do things the free and easy way, go with PostgreSQL and PostGIS.