MySQL does (did, at least; Postgres has been improving) replication better. Replication is really important for high availability, which almost everyone needs.
The irony, of course, is that a single Postgres server is frequently (IME) more reliable than multiple MySQL servers even when the latter is setup for HA.
In addition, replication is the next thing where PostgreSQL is vastly improving (according to their road map).
Also note that if you want to trade some of the ACID properties for better performance and replication, the so-called NoSQL databases (CouchDB etc) seem to be a better trade-off than, say, MySQL with MyISAM instead of InnoDB.
The irony, of course, is that a single Postgres server is frequently (IME) more reliable than multiple MySQL servers even when the latter is setup for HA.