I think this one depends on the age group you are going with.
IF you are going with adults, you will find much more to do at DHS than at DAK. I have never spent more than 3 hours at DAK, and even that is pressing the outer limit of how much I can tolerate there.
At DHS, some of the shows don't even start until the afternoon -- the car stunt show starts in the afternoon; at entry time you can fastpass either Tower of Terror or RockN Roller coaster -- but by that point, if you want to do the other e-ticket, Toy Story Midway Mania, your return time isn't going to be until after 2:00 even if you get a pass by 10 am...The Tram Tour itself takes nearly an hour -- my all time favorite Muppet Movie 3D adds another half hour....I can spend all day at DHS, I can't at DAK.
DAK doesn't hold my interest. I love animals, but there aren't enough of them there to see. You can do every single major attraction minus shows by 11:00, and then even get in one of the shows and be out by noon -- or TWO shows and be out by 1:00 and at your pool by 1:30 --