The word to describe the differeces between MySQL and PostgreSQL is divergent.
MySQL strives for fast select speed, using several small, fast queries being the preferred methodology.
PostgreSQL strives for SQL-92 standards compliance and meeting the ACID properties of a true relational database, as well as a very rich environment, like the ability to perform geometric functions on datasets in your SQL.
If you've got lots of text you are thinking of storing in flat files, you may find mysql is a great way to store that data in a more manageable format.
If you want to design an advanced database system with rules, triggers, stored procedures, views, unions, intersects, and other features, then you may want to use postgresql.
I you mainly want to learn SQL theory, stick to postgresql, or you'll be doing quite a bit of working around mysql's shortcomings in the feature department.
