We went to Animal Kingdom on May 24th and Zoo Atlanta on June 13th so I think I can compare the two of them fairly well.
At Zoo Atlanta, the only thing to see were the animals. At Animal Kingdom, there's a lot more to see and do other than animals. It's Tough to be a Bug, Dinosaur, The Lion King Show, Finding Nemo, Kali River Rapids, Expedition Everest to name a few. At Zoo Atlanta, you were just going from one animal area to the next ("oh, the bears are coming up next, then the elephant house"). You don't have that at Animal Kingdom. You see animals on the walks and in the Oasis and Discovery Island areas but they blend in very nicely (you kind of have to seek out the ones in Discovery Island). The two walking trails are set up to view animals but it's a straight walk through so you don't have to go from one area to the next.
But you can't really go to Animal Kingdom the first time and not go on the Safari. It's definitely NOT like a zoo. I don't know where in any zoo you can come around a corner and then see the African savannah right in front of you with native animals seemingly roaming around free like they would in real Africa.
At Animal Kingdom, the animals are free to do what they do naturally (within limits of course, they are in captivity). Even the bird show highlights the birds' natural ability - they don't ride bikes in the show.
I've been to many zoos in America and I don't consider Animal Kingdom a zoo at all.