There were a few reasons that MySQL took off when it did:
1) PostgreSQL was really, really slow at the time (PG < 7)
2) MySQL for simple select statements was (and is) really really fast
3) Wordpress used MySQL
MySQL is great for simple stuff. If you are doing only simple selects, and the thing you care most in the world about is simple scanning speed, MySQL may in fact be right for you.
But anytime you need your database to be more powerful, it is almost always dwarfed by PostgreSQL. PG has long left its slow days behind it. Even more importantly, complex queries are MUCH better to handle in PG. The query optimizer in PG is actually pretty amazing. I don't think MySQL even has anything close. PG allows full-text querying, searching, etc. in a native fashion. It has a ton of great extensions. It fully supports full programming languages when building functions.
Anyway, if you are only doing simple selects, then perhaps MySQL is all right. If you are doing anything else, use PG.
Jon