Animal Kingdom if you want to stay and enjoy the resort, but Old Key West if you want head out to enjoy shopping, dining, and entertainment at Disney Springs.
If my wife and I wanted to do a getaway and just relax at a resort (and not leave)....it would be Animal Kingdom. You have animal viewing areas, great restaurants, pools, and various quite spots on property to enjoy. You really don't need to go anywhere for entertainment. The animals are fun to watch.
If we wanted to getaway and are good with leaving the resort (for entertainment)..it would be Old Key West. You can relax and unwind at Old Key West, but there is not much going on unless you go to Disney Springs which has a TON of things happening.
Either way we love both resorts and would be very happy to stay at either.....so it would really just depend on what type of stay you are looking for. They are both outstanding.