9 days is enough without the event, but if you REALLY want to I'd say Villains. Don't get me wrong, I prefer AK as a park by far but DAH at AK just doesn't offer as much. It's basically designed for you to ride a bunch of rides over and over again, and in a park that is more than it's rides, I don't see it as good value. Most of the time you won't get on Kali, it closes before 7pm (I think). No Lion King, no Nemo - their last showtimes are before 7pm. Trails are closed at sundown so you'll have to pick one to go on I think before both close if you arrive at 7. It's just not worth it. AK isn't just about rides.
Villains, however, seems to be really worth it. In multiple reviews I have heard people say that the amount of rides they got done during the event is equivalent to or more than the amount they normally get done in a full day at MK. PLUS there's the special entertainment. Very much worth it.
Save a full day for AK where you can actually get everything done. Get a FP for FoP or arrive early. DAH at AK isn't worth it while Villains is. In fact, you could probably substitute a full MK day for Villains.