AWS RDS MySQL vs Aurora
The technical differences are summarised nicely in this SlideShare - http://www.slideshare.net/AmazonWebServices/amazon-aurora-amazons-new-relational-database-engine
It's really quite a different architecture/implementation under the covers from standard MySQL, and one that is fundamentally closed.
Amazon are being coy about the extent to which the front end is a MySQL derivative or a complete rewrite that is protocol-compatible - see http://www.theregister.co.uk/2014/11/26/inside_aurora_how_disruptive_is_amazons_mysql_clone/?page=2 - but it looks likely it's at least a major fork with lots of new code. It will have different bugs from the main MySQL releases, which users will be reliant on Amazon to fix. A distributed transactional database backend is a complex thing to write, and while Amazon have some of the best engineers in the world for this sort of system, it's still quite new.
It relies on a completely new Amazon-specific multi-tenanted storage backend, and the updated software isn't freely available as open source, so you can't just download it and run it on your own servers. It may diverge over time (e.g. years) in terms of functional features supported, meaning that code developed against Aurora may no longer work against mainstream MySQL releases, providing a risk of increased lock-in to Amazon.
Regardless, especially if your application needs them, the performance, low replica lag, scalability and recovery time reductions over standard MySQL look pretty compelling in the short term. The lock-in and costs are certainly much lower than with, for example, Oracle's Exadata - which is really the class of solution that Amazon are targetting.
Aurora is 5.6 compatible so if for some reason you need something below 5.6 you wouldn't use it. Also Aurora only supports innodb so if you utilize and need myisam tables then you would use MySQL