my rule of thumb, based on bone-headed decisions in the past:

if you think it might be nice to use a database, but you're not sure, and you might be able to get away with just flat file, use MySql.

if you know you need a database, and you know you are going to be using it in an 'advanced' way, but think you might be able to get away with MySql, use Postgres.

otherwise use MySql

when it comes down to the actual interaction with perl though, DBI makes both pretty easy, once you climb a pretty small learning curve. (assuming you know exactly what SQL you want executed)