We use postgresql at http://massify.com

I don't have enough experience with MySQL to be objective. I chose PostgreSQL because it had a feature set relatively on parity with Oracle and the other big boys. So far I haven't been disappointed.

Well, except for tool support. I'm still looking for a good schema diff tool for it (something as brilliant as SQL Compare by red gate) and a good ER tool (something as simple but functional as Enterprise Manager for SQL Server).

Otherwise, I really haven't considered looking at anything else.