I have experience with Oracle, Postgres, MS SQL Server and DB2.
Postgres is in the same range of relational enterise SQL database engines. Postgres offers even Oracle PL/SQL compatible syntax, so you can think of Postgres as the Linux of relational databases. (Linux is a clone of Unix). If you need advanced SQL syntax, XML support, complex triggers, inlined procedural code, GIS, etc look no further than this and choose Postgres. If you just want to hit your DB with thousends of connections from your web application frameworks and public APIs or think of easy clustering, it might be a good idea to add a caching layer in-front like memcached/redis or read on... (as the forking model doesn't scale that good)
And then there is a unique database-software with a common SQL dialect that supports dozends of database engines. It's called MySQL and it supports plugin-engines like InnoDB (default, true web scale, very fast), ISAM (old 1980s style features, very fast), etc. MySQL can handle many concurrent connections and InnoDB is really good, that's why it's a very good fit for web apps, using basic SQL features and used by Google, Twitter, Facebook, etc as a main production database.
And there are NoSQL databases that have different kinds of features like MongoDB/RethinkDB, Lucene (Solr/ElasticSearch), Hadoop (HBase, etc), Cassandra, etc. - they have often just basic SQL-like query language or non at all, but a custom API to interact with the datastore. Those domain specific solutions are often very fast for certain use cases. Some have limited index support, limited join support, transactions, etc. so the it really depends. E.g. for JSON datastore and full text search, those are ideal solutions.
We would need a database guide that highlights the common open source database engines. And provide a transition guide and compatibility matrix compared to legacy binary blob database engines - the real competitors to open source. People in the open source communities are often fishing in other communities and try to convert them - instead look no further than your corporate colleagues and enterprise fellows and try to convert them away from their rusty databases.