Pirates spent a LOT of money on their set and it really shows. It is very elaborate and cool to look at. That is the good news. Unfortunately the elaborateness of the set detracts from the show, IMO. The show itself is hard to follow, especially when it is not directed specifically at your section. Some of the actors are very easy on the eye, but their dramatic skills are a bit lacking.
Of all the dinner shows I've been to, Pirates was the worst as far as food goes, IMO. Some of the stuff was unrecognizable except for the servers identifying it for you.
Your DD might enjoy the show b/c of the audience participation but I really don't think the show or food compares favorably with either Dixie Stampede or Arabian Nights. You mentioned that you've already been to both of those shows, but did you see Dixie Stampede during the holiday season? They do a wonderful Christmas show featuring a living nativity scene that is just beautiful.