What are the advantages of going with AWS Aurora DB with Mysql backend over AWS Aurora DB with Postgresql backend? It's great if someone can share your experience or point out a document.
You got it wrong. Aurora is its own backend, but it comes with MySQL compatibility:
Amazon Aurora is designed to be compatible with MySQL 5.6, so that existing MySQL applications and tools can run without requiring modification.
The PostgreSQL compatibility is only available as a preview yet, in only one AWS region, after sign-up.