We have seen up to a 2x improvement in Postgres' throughput after tuning it with OtterTune over the default Amazon configuration. Here is an overview of how OtterTune's algorithms work: https://aws.amazon.com/blogs/machine-learning/tuning-your-db...

Hit us up to see if we can do the same for you: https://ottertune.com/demo.html

RDS takes care of 1/3 to 1/2 of the configurations, particularly around hardware related options. However, since postgres uses MVCC, it has a lot of tuning options around autovacuum and replication that impact performance. This is even more true if you have access patterns that don't take into account postgres' MVCC (are you updating 10%+ of large tables daily, triggering autovacuums?) but which would be fine with mysql