PRO: fairly easy syntax good management tool (phpmyadmin) easy to integrate and use with PHP, Ruby etc. very common therefore lots of tutorials and howtos CONS: performance bad or missing RDMS...
The main difference that I see is Postgres' advanced support for things like Views, Stored Procedures, Transactions and other more advanced database functions. This is not to say that MySQL does not...
Although My SQL supports primary keys, it doesn't support the use of foreign keys, meaning it doesn't have all the Relational Features of Ms SQL, which is considered a complete Relational Database....
While MySQL does not have a true database engine it does perform well for small deployments.
The advantage; its free.
The disadvantages would take days to write.