I've never sailed Carnival.... In the last 5 years, my only cruise lines have been NCL and
DCL. And the NCL was not the absolute newest ships. But for right now, with an 8 year old and 10 year old, my very very strong preference is DCL, and it is worth the extra cost:
1 -- Amazing kids clubs, with great hours. I know NCL hours are rather limited, with "closing" for lunch and dinner. And I know most cruise lines charge extra past 9 or 10 pm. But DCL.. 9am to midnight, come and go as you please. Great for the kids AND great for the adults.
2-- Service, true to the Disney brand. The staff just seems better trained in terms of customer service, the wait staff speaks better English, etc.
3-- Disney theme -- Certainly not critical to a great vacation, but there is something to be said for being surrounded by Disney characters and princesses, Disney music, entertainment, movies. The shows are top notch, for the whole family.
4-- "Current" movie theater. So for our August cruise, the kids will likely get a further chance to see on the big screen, Avengers, Cinderella, Monkey Kingdom, Tomorrowland, Inside Out, and/or Ant Man. They will likely have seen most of those movies in the theater before, but not all. Heck, that I looked at the list, I'm looking forward to getting to take in a late night or early morning movie.
5-- No casino. Other lines devote a ton of space to the casino, and assume it will use up much of the adult time on the ship. With no casinos, Disney ships have the room for the movie theater, and they concentrate more on other activities for adults and kids.
6-- Ability to segregate away from the kids. At least on NCL, it felt like kids were everywhere, all the time. Whether my kids, or other kids. They made it impossible to enjoy a pool or hot tub. Even the bars were filled with kids. Disney seems to do a better job of truly creating adult-only areas.
7-- Included soda, lots of included TV stations/on demand movies.
My last 2 NCL cruises, were in suites. Great butler and concierge service, huge cabins. A balcony cabin on DCL is similarly priced to a suite on NCL. But now, I strongly prefer the Disney balcony over the NCL suite.