From the README, pg_rman provides point in time recovery (PITR) and maintains a backup catalog:

> The goal of the pg_rman project is to provide a method for online backup and PITR that is as easy as pg_dump. Also, it maintains a backup catalog per database cluster. Users can maintain old backups including archive logs with one command.

Having used pgBackRest in production, I find it to be painful to setup and manage.

If you have a centralized backup repo, you have to install pgbackrest both on DB server and the backup repository.

The package version has to be exactly the same minor version between the DB and the repo, else backup fails. If you install a new DB, and the PG common repo no longer has the old version (and no one kept a copy of the rpm locally), you then have to update backrest on all the existing servers.

pg_dump is a completely different category as it’s a machine portable logical backup. You can restore an older version backup to a newer version installation as an upgrade mechanism.

Just about every other backup program concerns itself with binary backups which generally facilitate point in time recovery as well.

Both have their place and it’s common to have both done on different schedules. Though purely logical backups get interesting at scale as it literally has to run a SELECT * on every table from scratch each time.