Firstly take a look at this recent AWS April 2016 Webinar Series – Migrating your Databases to Aurora and the  AWS June 2016 Webinar Series – Amazon Aurora Deep Dive – Optimizing Database Performance session lead by Puneet Agarwal

Here are the main reasons I would look into for choosing AWS Aurora over AWS RDS MySQL

1. Faster recovery from instance failure (X5 times or more vs. MySQL)
2. Consistent lower impact on the Primary replica
3. Need additional throughput (theoretically X5 times for the same resources vs. MySQL). This was achieved by decoupling the cache and storage sub-systems and spreading them across many nodes as well as performing log commit first while DB manipulation is done asynchronously.
4. Using or can migrate to MySQL 5.6
5. Comfortable with the Aurora I/O mechanism (16K for read, 4K for write, all can be batched if smaller)
6. Get more replicas (maximum of 15 vs. 5 in MySQL)
7. Prioritise recovery replica targets and set replicas with different size than the master
8. Need virtually no replication lag – since replica nodes share the same storage as the master uses
9. Able to decide about encryption at rest, at DB creation
10. Accept working with the InnoDB engine alone
11. Want to eliminate the need for cache warming
12. Allow additional 20% pricing over MySQL to gain all the above 🙂