The big production is NOT on each cruise. Usually move it around from RCL ship to RCL ship. It's done with professional actors, etc. The dinner one is by crew members. Both are good I'm sure, I know the big production is great.
Here's link to the production company, they should have a schedule of which ships are next for the Whodunit mysteries.
Let us know how the dinner theater one goes if you do it.
We've twice done the "regular" Murder Mystery . It is ship's staff that do it. It starts in one of the bars upstairs and eventually works it's way to Chops. We do like doing it however when we attended the one on the Mariner, it was completely marred for us by our waiter. We had been put in an extremely bad place (I believe they overbooked) and at least 5 times I was asked to move one way or the other so the actors could get back.