I've been to HH every year for the last eight years, my DH, the last twenty! It's the nicest tropical escape in the U.S. imo. I haven't stayed at the Disney resort, but I hear they have loads of planned activities, so much that you can be busy every minute of the day if you wish!
Some non Disney activities we enjoy are; Beach walking, bike riding, golfing, swimming, alligator hunting (just for pics!) outlet shopping, exploring out of the way dining and shopping, resort hopping, jet skiing, dolphin cruises, crabbing, fishing, and last but not least, relaxing poolside!
Some years we are more exhausted after our week than when we go to WDW!
We love it there so much we're hoping to live there one day. It really is a wonderful island.