I see a titanic advantage of PostgreSQL over MySQL: the license.
http://www.postgresql.org/about/licence
http://www.mysql.com/company/legal/licensing/commercial-license.html
Would you like to use the database for commercial purposes?
To my way of thinking, the Berkeley style license is the best of all
worlds.
Other than that, the Oracle/Sleepycat stuff is a little worrying.
But both products have advantages and disadvantages. If you build a
standards based interface to the database, then you can always switch
from one to the other {or some other DB altogether} with relative ease.
You'll find rabid fans in both camps, of course. I'm a PostgreSQL fan,
so anything I say should also be taken with a grain of salt. Simply
put, I like PostgreSQL better.