Ye' old general discussion board. Basically, for everything that isn't covered elsewhere. Come here to shoot the breeze, shoot your mouth off, or whatever suits your fancy. This forum is not for asking programming related questions.
PostGreSQL is designed as a Object Relational Database Management System that strives for a very high level of compliance with the SQL specs. MySQL is very non-compliant and is typically willing to trade off features for speed. For some people thats a fine trade.
Some of the features PostGreSQL offers that I beleive are lacking/weak in MySQL:
user defined types, functions, aggregates, operators
from clause join syntax
views, rules, triggers
integrity constraints (more complicated than simple foreign key ones)
All of these are features I use daily. Some of them have no reasonable workaround other than implementing in application code things that a DBMS should do for you.
Generally speaking an out of box install of PostGreSQL under-preforms MySQL when using non-transaction tables in MySQL and doing read only.
If you use MySQL's transaction tables and have moderate updates/insert/deletes the difference in preformance tends to become much less. If you allow expert "tuners" to help you configure your DB the difference normally vanishes.