Postgres is cool, I like it a lot. It has more features than MySQL but has a slightly higher learning curve than its cousin.
On the flip side, MySQL’s SQL parser is a lot less strict which makes getting to grips with MySQL easier, but the MySQL licensing is interesting and with Oracle being its owners, people are more wary of using it in a commercial setting these days. PostgreSQL has a much more liberal license which makes it a more appealing prospect for commercial reuse.
For raw power, I’m a huge fan of Exasol, its an amazing database for processing high volume data quickly, but it costs a few quid if you want to deploy it properly.