They are really 2 different kinds of shows and as such are difficult to compare. Like trying to compare Beaches & Cream to the Yachtsman. Both are good at what they do, but they don't do the same things so making comparisons is difficult.
At HDDR, you'll get a meal ( not fancy ) and all of the beer or wine you can drink in addition to the show. It's corny, but it's supposed to be corny.
On the other hand, at Cirque, you'll pay as much or more ( depending on where you want to sit ) and still have to pay for dinner somewhere on top of it. It's a show everyone should see, but as with HDDR ( too corny for some tastes ), not everyone likes a circus.
In a perfect world, I'd say do both, but if it's not possible, I'd go with which ever one sounds more appealing to you and your party.
Good luck!