I can't answer about the whole menu- although we certainly had more seafood and more international dishes on the Carnival Med cruise I did than the Carnival Mexican cruise. But they have a dessert- warm molten chocolate cake- that's standard on all ships I think. I've found recipes for it on the internet. There are other standards- lobster tails on formal night, for example, and steaks any time. But the meals on the Med cruise were really fabulous!
I believe that every Carnival ship follows pretty much the same menu on a day by day basis. The Med/Euro cruises may change it up a bit to satisfy their European based passengers.
However, every Caribbean ship is serving the same thing on a monday, tuesday, wednesday, etc. The shorter cruisers cut out a day here and there but for the most part, it is the same menu across the board.
(cruzin' solo by design)
Freedom ('09), Imagination ('08), Victory ('08), Destiny ('08), RCCL Navigator ('08), RCCL Majesty ('08), Glory ('07), Liberty ('07), Fantasy ('07), Destiny ('06), NCL PofAm ('05), Fascination ('04), Victory ('04), Fascination ('04), RCCL Voyager ('03), Fantasy ('99)