Last time i checked (2 days ago) mysql didn't respect FK constraints!
Mysql is a nice toy for the web, but not something a large organization would want to rely upon. Not something that could model complex concepts, and relationships.
PostgreSQL on the other hand, seems to respect data and the semantics of the schema in a serious way. In other words, in PostgreSQL, when you say commit, its a commit, when you insert, it *will* check for referential integrity, when you use NULLs, then the DB will handle them as is dictated by the specs and *NOT* based on what the majority of users wants or thinks.
Not to mention those 30+ lines of a single query, which returns the *correct* result in a fully explainable/deterministic/predictable manner!
IMO, PostgreSQL (not to talk about the commercial versions of it), can be a replacement for Oracle in 90-95% of the occasions, out of the box.
And as other people have said, when you learn postgresql, you learn how to be a real DBA. If you learn a toy like sqlite, then it will be equivalent of knowing lets say ms-word or ms-excel.