I've done both and love both, but if I were to pick just one, I would go with DAH. Both have minimal crowds, but DAH gives you most of the MK rides open where as MK is a handful of Fantasyland only. We like EMM to see how many times in a row we can ride SDMT, so for that it is great. But, DAH gave us the chance to ride just about every open ride in 3 hours, which was amazing and I will do it again any time it is offered on our trip.
Things to consider when choosing though is age of your family and if you have very young kids who would not be able to stay awake for DAH, then obviously that would not be the way to go for your family. Conversely, if waking your family up super early on vacation is not for you, then skipping EMM would be best. Also, EMM includes breakfast, and a pretty decent one at that, so cost wise you could argue you get more value with that than just some snacks with DAH.