I have done both.
Hoop Dee Doo was absolutely not something I would have chosen, but it was recommended by our TA as a "must do". So we trusted him, but were skeptical. WE LOVED IT! Was a total highlight of our trip!! It was so cheesy, in the best way! We laughed and felt like kids again! The food was a real surprise, too--for "all you care to eat" en-masse food, we didn't expect much. But it was yummy. And I liked the sangria--not too sticky sweet like some can be. We went during a low season, and there was not even a fully seated floor, and no one in the balconies, but it still felt lively! I can only imagine what energy a "full house" creates!
We were going to do HHDR again the next trip, but decided we should try the Luau. We had heard some mixed, mostly bad, reviews of it; but we figured it could not possibly be as bad as some of the reviews we read. But it was WORSE! The food was only okay, the first half of the show is agonizingly bad (cheesy in a BAD way), and our server was surly and inattentive. We had front row seats, which was nice, but I could see many places where the view would be awful. The server never got me a second drink, and dumped one on me, breaking the glass at our open-toed feet. Didn't apologize, only brought a towel when we asked her to (not automatically and swiftly), and didn't clean up the glass. Just the pits. The rest of the trip, when something was really bad or embarrassing, we would say "That is *so* Spirit of Aloha..."
This trip we are going back to Hoop Dee Doo, and are treating our friends to it along with us. It is their honeymoon we are meeting up with them on, and I can't wait to share the laughter and yummy food with them!