PG is far superior to MySQL. Incremental backups are a default on PG, while on MySQL is far more sketchy. This thread: http://www.quora.com/What-are-the-advantages-and-disadvantag... has some thoughts as well. Redis is great.
There is a significant body of existing code and tools which assume MySQL, so I often use it for that reason. It's also not always an either/or proposition; there's usually nothing stopping you from using X for user accounts and Y for inventory tracking.