Voyage of the little mermaid in years past was one of the best produced shows at disney. having 2 girls, we have been to this show more times than I can count. It has not changed, AT ALL, since it opened in the 90's. But even for a 20+ year old show, it is still pretty cool. Even for boys.
BATB stage show is a condensed musical version of Beauty and The Beast. They hit the 4 or 5 major songs from the movie. But the show itself does not have the technical accomplishments that Mermaid has.
Really, both shows stand or fall on the strength of their lead actors. A good Belle and Gaston make BATB a good show. Band ones make it a bad musical. Same for mermaid.