Highly debatable, but I have to go with MySQL here. Although, I have to confess, my experience with both is limited and probably a bit outdated too.
Let me start out with some specifics that I know of.
MySQL provides a smaller footprint, is better supported by the community (i.e. numbert of pages written on the subject) and is supported by most providers. It has also the benefit of tools like phpMyAdmin that are a bit more developed than the equivalent tool phpPgAdmin.
On the other hand, PostgreSql has a lot more features which means that you can omit the tedious task of coding helpful functionality by yourself.
Both databases are free to use, although the licensing-model differs. That would be a nice topic for another debate though.
Both databases are quickly expanding their possibiities, PostgreSQL is getting quicker whereas mySQL is getting more fully featured. My guess is that in a few years time, neither is significantly better than the other.
So, in the end, my conclusion is only build on the fact that mySQL seems to be more widely accepted by providers which makes your website more portable along them. And for that reason and that reason alone, mySQL get's my vote.