PostgreSQL is probably the most advanced Open Source database providing the widest range of features a relational database can have, including transactions, triggers, views, and sub-selects. It is used in a large number of high-end installations world wide. As we find PostgreSQL the strongest contender when selecting database for a project we are providing support and training for it.
MySQL is a very popular low-end database. It is usually faster than PostgreSQL but it is lacking some of the feature that a high-end database can provide. It is very popular among PHP developers and it can prove to be the right solution for projects where speed is more important than data integrity. As we find MySQL as a good solution for some of the applications we provide support and training for this database as well.