They are both excellent tours! It all depends on what you'd rather see. The Backstage Safari tour is entirely backstage, which gives an excellent view of the behind the scenes activities, the animal enclosures, and the feeding and health of the animals. The Wild by Design is a newer tour that takes place entirely inside the park, where the tour guide takes you around and points out a lot of the inside stories and secrets about the various areas of the Animal Kingdom. You spend a lot of time outside in both tours, so I would try to pick a cooler time of year, if possible.
I would highly recommend both of them. And besides, you get a pin at the end of both tours, which if you don't want, I would be more than happy to trade you for!