Well, this is an hard question, even if PostgreSQL it's more mature and support all the most modern features, MySQL in the last 2 years reached the same level. PostgreSQL is working to improve performance and to add new valuable features. MySQL is working most of all on adding new features and in bug fixing.
Even if PostgreSQL is still slower then MySQL, it has some advantages then MySQL, like unlimited number of indexes (MySQL 64)
PostgreSQL is completely open source. MySQL not, it has two licenses, one commercial and one open.
I strongly advice you to take a look on this comparison
http//www.encorewiki.org/display/encore/Open+Source+Databases+Comparison
And to read the features list and choose the DB based on your needs
http//www.postgresql.org/about/press/features83
http//dev.mysql.com/tech-resources/articles/mysql-storedprocedures.html