From my understanding, Aurora is a modified MySQL with a few components substantially rewritten and a new, log-structured storage engine added that is well integrated with Amazon's storage infrastructure (volumes auto-grow, quorum is handled at the storage layer, replicas are just caching views on top of shared, replicated storage). MySQL has support for multiple storage engines over a relatively simple API, while Postgres is tightly integrated with its storage engine.

In addition, MySQL just has a lot fewer features and points of extensibility, so it would likely be easier to support.