Can only comment on Carnival. We are a family of 4 (kids are now 10 and 12).
We have sailed 2x to date and are awaiting our 3rd.
We started out with 2-5 night cruises. Thought 3 might be too short if we enjoyed it and 7 might be tooo long if we didn't. Loved it so much we have booked our 3rd and it is a 7 nighter.
We are hooked. Great value for the family. Lots for the kids to do with Camp Carnival. They have met some great kids and are still keeping in touch.
Have compared the cruises to taking the kids to Disney or Universal. Can't beat it. Your food, lodging and entertainment are all included in your cruise price. Only extras were soda cards and shore excursions. Meals were a great time for the kids to try different types of things they may not try at home.
Good luck on your search. Hope you find a line that works for your family.
Out of your list, for cruising with families, I would say Royal CAribbean. They offer a great kids program and have lots of activities, for everyone in the family. Be sure to check out one of the Voyager class ships for the most activities and next year a new class, Freedom, even larger than Voyager class ships.
Have sailed 5 times with RCCL and 6 with Carnival. I would recommend RCCL
for families. Their Voyager class ships offers the best activities for families.ie. Ice skating, rock climbing, mini-golf and inline skating. Just to name a few