We have been on one Carnival cruise (July 2011) and 9
DCL cruises since November 2013 and we can justify the cost quite easily. We have two teens and my husband and I that sail at various times of the year, but frequently in the fall (Septmeber is our favorite BECAUSE of the lower rates) However, we have also sailed in January, April, June, November and December.
We can justify the price difference between the two cruise lines for a few reasons that work for OUR family. But if you feel that you would have a hard time justifying the cost, then would you really have a great time or would you worry about how much more you spent?
1. On Disney the cabins are bigger ...we stay in the verandah cabin on Disney. One cabin fits all 4 of us comfortably. On Carnival, I got 2 Oceanview (window) cabins side by side. I was traveling with my Mom and 2 kids back then as my husband could not get away. The cabins were small to the point where you had to wait until the other person in the cabin sat down or pressed themselves against a wall. lol.
2. Split bathrooms on Disney are very good to have. While my daughter (now 14) gets ready in one, someone else can use the other one. LIke my 13 year old son for example.
3. Disney entertainment venues are awesome and always have something going on that is age appropriate for kids and adults. We saw one show on the Carnival ship that was comparable to a strip show in Vegas with humor that pushed the envelope for a "kid friendly show. The actual adult show was really raunchy...and I do not blush easily...but I am pretty sure I came out looking like I had some five alarm chili.
4. On Carnival, the excursions were not handled very well and I never really felt comfortable leaving the ship for too long. Their cab/taxi services were not controlled in any manner and there was a lot of pushing and shoving happening. Not cool. My Mom is /was in her 70's and my kids would have been 9 and 10 at the time of sailing. It was all I could do to make sure that they did not get wound up in a crush of people. In Freeport we just turned around and got back on the ship. Which worked out great because it was really quiet on the slides. And in Nassau, we did the Dig tour of Atlantis and it was up to us to find our way over to the other side. I like the Disney excursions because, they have a really good handle on keeping people together and organized.
5. Food and service on Carnival is not the best, but the food was edible and the wait staff seemed friendly. We had a different person every night so no real connection was there. I think I saw our room stewards once in the 4 night cruise. As you know Disney has this down with rotational dining and very attentive (at least all of ours have been) cabin hosts/hostesses. You feel like you are more than a body filling up space with Disney. Even though you really are.
6. Kids clubs with Carnival felt like a free for all. I never really felt comfortable leaving the kids there but figured it would work out since they both were in the same age range) They went once and never went back. It was crowded and not very organized. But you know what? Sometimes my son doesn't want to go to the kids clubs on Disney either but my daughter will spend quite a bit of time there if she makes friends early enough. It irked me about Carnival but the kids and I had lots of fun hanging out together anyway so we were okay.
Ultimately, you have to justify it with your family and traveling companions. Anyone else that might question you about sailing on Disney and how expensive it is, is not really important. People spend their vacation money in ways that make them happy. That and family time is the most important thing.
You can have family time on Carnival just as much as you can on Disney, but you might find Disney more comfortable.
Enjoy your upcoming cruise!
Myself for the cost even though I want to do another family vacation on 
)= $4900. Off season. Better, but still prices rising like mad.
