Aurora is expensive, but it's a huge instant speedup and easily worth the cost for anyone with a production application that occasionally hits performance limitations on traditional MySQL.
That said, it is based on MySQL 5.6.10, so we are missing some features like online DDL from 5.6.17. Many bugs from 5.6.10 have been resolved upstream but are still present in Aurora.  It's also subject to the usual limitations of RDS (no SUPER, no access to the binary database files, no innobackupex).
I know MySQL has made some half-hearted attempts to make headway on this front, but it has completely changed the way I model certain parts of my data.
Unless you mean that the other way around, in which case I don't know what key features of Aurora I'm missing (besides price & performance).
Some can't live without Aurora anymore ;) - they start their projects with MySQL(even thought they prefer Postgresql) to be Aurora compatible, just in case they need it.
The comparisons I could find didn't seem to be very favorable to Aurora (mainly that the claimed 5x improvement does not show up in the benchmarks)
We cut our costs by about 40% after the switch and saw about a 20% boost in speed. RAM usage was lower too.
One of the biggest savings is that you don't need multiAZ since your data is stored redundantly. You don't have to worry about failover because the restart time is < 1 minute anyway. The other thing is that I can stop having to keep an eye on disk usage (and paying for unused space) since it just grows as needed automatically.
The man hours alone that we used to put into actively watching and tuning that DB have just vanished as has almost the entire sysadmin burden. That project was already on MySQL too which made it an easy move too.
I wish they'd do something similar for PG too.
Look at all the comments here about new features and bug fixes introduced upstream but missing in 5.6.10 (online DDL, JSON, etc.).
We already have Oracle's MySQL, MariaDB, WebScaleSQL, MyRocks (Facebook's MySQL with RocksDB and DocStore), Percona Server for MySQL, and now Aurora. Each version has its own features and peculiarities. The ecosystem is too much scattered.
Aurora is based on MySQL 5.6.
They had a deep dive into during the last re:invent.
Also a good bit of video of Vogels talking about Aurora.
This could be really important because some applications end up relying on MySQL oddities even with good willed developers.