We've been using PostgreSQL since the very early days of Zulip, but we actually didn't use it from the beginning. Zulip started out as a MySQL project back in 2012, because we'd heard it was a good choice for a startup with a wide community. However, we found that even though we were using the Django ORM for most of our database access, we spent a lot of time fighting with MySQL. Issues ranged from bad collation defaults, to bad query plans which required a lot of manual query tweaks.
We ended up getting so frustrated that we tried out PostgresQL, and the results were fantastic. We didn't have to do any real customization (just some tuning settings for how big a server we had), and all of our most important queries were faster out of the box. As a result, we were able to delete a bunch of custom queries escaping the ORM that we'd written to make the MySQL query planner happy (because postgres just did the right thing automatically).
And then after that, we've just gotten a ton of value out of postgres. We use its excellent built-in full-text search, which has helped us avoid needing to bring in a tool like Elasticsearch, and we've really enjoyed features like its partial indexes, which saved us a lot of work adding unnecessary extra tables to get good performance for things like our "unread messages" and "starred messages" indexes.
I can't recommend it highly enough.