I was giving this a bit more thought and decided to break it down by attractions.
When you consider rides, there are five at DHS: Tower of Terror, Rock n Roller Coaster, Star Tours, Great Movie Ride, and Toy Story Midway Mania. The last two mentioned have no height requirement. You must be 40" to ride Star Tours and Tower of Terror and 48" to ride Rock n Roller Coaster. To compare, Animal Kingdom has six rides: Kilimanjaro Safaris, Expedition Everest, Kali River Rapids, Dinosaur, Primeval Whirl, and TriceraTop Spin. TriceraTop Spin and the safari have no height requirement. Kali has a 38" requirement, Dinosaur has a 40" requirement, Everest is 44", and Primeval Whirl is 48". So, both parks have two rides that your daughter can ride. I doubt that most of the family will enjoy TriceraTop Spin and it's just like Dumbo or The Magic Carpets of Aladdin that you can do at Magic Kingdom. The Safari is unlike anything you can do at any of the other parks, though. Great Movie Ride doesn't get a lot of fans, but it's been my favorite since my first trip when I was 8. When we first took my daughter when she was 2, she continually asked to do it. Toy Story Midway Mania, as another poster said, is one of the most popular rides in all of Walt Disney World. So personally, I'd give the edge to DHS regarding rides for your daughter/the whole family. Now, as far as thrill rides go, Everest and Rock n Roller Coaster are probably tied. Both are very fun and high energy. If you like coasters, you will love both of these. If you don't like coasters, neither one will do anything for you, but the queue for Everest is, in my opinion, significantly better than the one for Rock n Roller Coaster. I find Tower of Terror to be much more fun than Dinosaur. Dinosaur isn't bad, but I think that Tower of Terror is more of an adrenalin rush. And, it is also my opinion that Tower of Terror is the best themed ride in all of WDW. From the moment you enter the gates to get in line, you are engulfed in the theme of the attraction. It's pretty darn great. Primeval Whirl is not something I can do without getting sick, but it is your basic wild mouse-style ride. Theming is quite lacking. So, for thrill rides for the bigger kids, I give the advantage to DHS, as well.
Regarding shows, both parks have some great ones. DHS has Journey of the Little Mermaid, Beauty and the Beast, Indiana Jones Epic Stunt Spectacular, Lights Motors Action, and Fantasmic. Fantasmic is my favorite show in all of WDW. I absolutely love it and recommend it to just about everyone. Little Mermaid and Beauty and the Beast are also quite good and very similar to the movies. If you like the movies, you will like these shows. Indy can get boring for kids and LMA can get boring or can be something that the kids really love. It can be pretty polarizing, I've discovered with people either really loving it or really not caring for it. Animal Kingdom, on the other hand, has Flights of Wonder, Festival of the Lion King, and Finding Nemo the Musical. If you liked Finding Nemo, you will likely enjoy the show. It does have some music that isn't in the movie. Festival of the Lion King is truly fantastic and has a lot of audience participation. Flights of Wonder receives a lot of praise but really isn't for me. But then again, I live 15 minutes from a zoo with a bird show so it wasn't all that special. I give DHS advantage on shows, but have no problem understanding why someone would give it to Animal Kingdom.
Now with extras, Animal Kingdom does have the Pangani Forest Exploration Trail and the Maharajah Jungle Trek. The Trail gives you a great view of the gorillas and the Trek is great for seeing Tigers, but I was bored for most of the rest of both of them. The Boneyard can be a fun place for your daughter to play while your boys go on some thrill rides. At DHS, a lot of the extras are getting closed, such as the Honey I Shrunk the Kids Playset. But, the do have One Man's Dream which is a museum of Walt's life including his desk as a child, original Mouseketter costumes, original plans for Epcot, etc. and a short video on his life. They also have The Magic of Disney Animation and Animation Academy where you can learn to draw Disney characters, learn about new upcoming movie projects, et your picture taken with Sorcerer Mickey and some newer characters, and play around a bit. As far as extras go, I consider it a wash.
Then you have dining. DHS really doesn't have any spectacular counter service restaurants to speak of. The themes aren't phenomenal and the selection isn't very unique. An exception is at Studio Catering Company where they have turkey clubs, sloppy joes, and buffalo chicken sandwiches rather than just burgers and chicken nuggets. Table service restaurants are fantastic, though. Sci Fi Dine in is probably the best themed restaurant in all of WDW, 50's Prime Time gives it a run for its money, though. Both are very fun. Your daughter and 6-year-old would likely enjoy Play and Dine with the Disney Junior characters at Hollywood and Vine. Mama Melrose is decent food and provides you an opportunity to do a Fantasmic Dining Package which I highly recommend, especially if you are getting the dining plan (more food for the same credit). I'd stay away from Brown Derby with young children. Animal Kingdom definitely has the better counter service restaurants with Pizzafari having different themed rooms. Flame Tree Barbecue, while not fantastic, is just as good as anything on Sunset Blvd at DHS. It also has Restaurantosaurus which is standard burgers, sandwiches, and a mac and cheese dog, but we do like it. For table service, they have Rainforest Cafe, Tusker House where you can dine with the characters and experience some different foods at a buffet so you don't actually have to commit to something if you aren't sure if you will like it, and Yak and Yeti. Not bad table service restaurants, but I give DHS the advantage. Animal Kingdom, though, definitely has the advantage for counter service.
So, going off of all of these categories, I'm sticking with DHS instead of Animal Kingdom, but Animal Kingdom does have its audience and appeal. If you think that is more your family, go for it and I'm sure you'll have a great time.
