We have been going to Disney World nearly every year since I was 13 and now I take my kids. I have been to both parks and I would recommend Disney.
Universal Studies is fun, but it is just a theme park. Granted it is a big one with cool themed rides, but it is just a theme park. Disney is an experience. It is cleaner, the people are nicer and the rides are much more unique.
Magic Kingdom and Hollywood Studies both have roller coasters, action shows and more thrill rides than the other two parks. Animal Kingdom is like a big zoo, but they do have some thrill rides as well, including Expedition Everest.
Epcot is my favorite, but it does not have as many fast paced rides. Plus, each park has a pretty amazing final show at the end of each day.... except Animal Kingdom.
If you can afford it, I would suggest that you get the park hopper option, so you can switch parks if find that your current park is not what you wanted.
Disney is also known for doing everything that they can to make your vacation the best that it can be. So you could even call the hotel or Disney Rep and tell them your concerns, you might end up with special passes to a unique show or front rows seats as an incentive to get to to visit their parks instead of Universal.
Have fun!!