Is there any compatibility issue with Amazon Aurora?
We are running a couple of projects on Amazon Aurora  with no issues so far. Our largest project is a D7 project with many contributed modules, and a large amount of data being moved.

We've never noticed any DB related issues aside from normal MySQLisms. It's really transparent to Drupal. We use normal Mysql connection strings and zero core changes. 

Aurora is more expensive. A lot more expensive. It only starts at the db.r3.large tier, and works out to a monthly (non upfront rate of 0.190 per hour). So the price difference must be considered.