Hi Jose, that is a very good question. Many people tend to make the discussion about durability or performance, when in fact most people don't have performance issues. I believe if you want to figure out, what database to use, you need to first figure out what our application's requirements are. If you are building a browser based application that is running locally and you don't need anything but integers, floats and chars. Go with SQLite. If you run a more sophisticated application, maybe follow a SOA based architecture or want to use JSON, UUID, HStore or Arrays; different indices, stemming and database triggers; not to forget PostGIS. Use PostgreSQL. If you have a BI team that needs to build ETL processes, definitely use PostgreSQL.
Bottom line, if you need a simple structured ACID conform data store, use SQLite. If you need a database with plenty features and umpf, use PostgreSQL. BUT ultimately it comes down to what you are most comfortable with. I have been using PostgreSQL for almost a decade and am