CruiseDad, I'll second everything penny3333 said. I pay particularly close attention to the shows as I worked as a musician for Princess many years ago. The shows are 1000% better than they were when I was backing them; of course there is no way you could have put on a big production on the original Island, Pacific or Sun Princess.
I think the dancers are the highlight of the shows--and I'm not just saying that because I know your daughter is a dancer. The dancers are the best, followed by, in my opinion, the lighting, the choreography, then set design and costumes. The musicians and singers are adequate, with an occasional stand-out guest performer. I saw a banjo player once that blew me away, in spite of the fact he was playing a six string, which I consider an abomination.
And yes, as Penny said, I see the dancers doing all the other things you mentioned.
I have not been on a Carnival cruise so I can't offer a comparison; but I can tell you I am very impressed by the level of professionalism, the enthusiasm and the energy of the Princess dancers.
The writing in the shows leaves a lot to be desired; the shows have become pretty formulaic and at times, even trite: but you didn't ask about that and it dosen't really detract from my overall enjoyment of the entertainment.