I have not cruised either line yet but have REALLY studied Carnival and Disney along with RCL. We are in the midst of planning a
Disney cruise but since I have studied them SO much I thought I would post some comments and suggestions that I hope would help....
travelocity has tons of cruise info. pictures, cabin sizes, itineraries, prices, traveler's reviews etc.... it was really helpful.
www.cruisemates.com has lots of info too - esp for family cruising.
these are the things that I looked for while figuring out what cruise I was going to go on...
pricing and staterooms - yes carnival is cheaper, esp the older ships but the newer ships that would compare to disney - are only about $150 less pp when I was looking (Sept 2005) for inside rooms. Balconies are a big price difference but I wasn't intersted in that. You also have to take the staterooms sq footage.
DCL have the biggest standard rooms and a split bath that families truly need.
kids entertainment - I have never really heard a vaild complaint for disney's kids clubs. I have heard there isn't as much to do for the teens but that wouldn't affect me (or you actually.) I have heard some poor reviews of some carnival ships kids areas. Disney seems to do more with the kids then just put them in a room and they seem to have much more activities all day and night to keep the kids busy. They don't charge any money either and stay open until 1am. Carnival charges $6/ hr per kid after 10pm so that could add up for you - if you want alone adult time at night. It also seems that disney has so much more family entertainment at night and really seem to separate the kids only areas, family areas and adult only areas well so that everyone is happy. Carnival tends to have a lot of adult entertainment and night shows but nothing too kid friendly.
adult entertainment - Carnival looks to have more adult night activites, shows, casinos and such. My dh likes to gamble and I do not so
not having a casino on DCL was actually a plus for me

and no worries about spending more money!! I have heard things pretty much shut down around midnight on Disney but Carnival keeps going all night. Crusing with kids, I can't imagine who can stay up much past that anyway and I have heard there is a lot of smoke and drunks on carnival that can spoil a night.
Food I have heard Carnival has really stepped up their food and seems to get great reviews but you will always find good and bad reviews for both shiplines. It depends on what you are really looking for. I have also seen people say that disney's food incredible and some that say it was subpar but once I looked more into why, this is what I found. Disney only has 4 course meals compared to other liners 6 course meals. I think disney realizes kids are aren't going to sit around for that. You can however order anything and as much as you want.You can look at some sample menus of disney food online too - it looks good to me!!! Not top line gourmet but better than most restaurants have. I have also heard the dining staff with disney is superior, esp with kids, compared to carnival. To me, that can make or break a cruise. Disney also has 3 separate dining rooms and you rotate to all 3. Something a little different and none of them look like the stuffy huge dining rooms found on most ships. disney also has palo's adult only restaurant which gets great great reivews. I can't wait to try it!!
As far as itineraries are concerned, Carnival does have a lot more to offer and many more ports they ship out of but then again, this is yuur first cruise so either the disney eastern or western could appeal to you.
So anyway, I am not going to ramble on anymore. It seems to me that your kids are at a good age for a Disney cruise. If you can spend the extra money, I would say go for it. Many say it is worth it and after doing so much research it seems to me like it is. I have been to disneyworld and
disneyland many times and the employees are always so happy and helpful and I love the feeling of being there. I want that kind of treatment on my cruise!! You said in your post you want it to be magical - nobody does that better than disney
Also - down the line when your kids are older they may not want to do a disney cruise - so try carnival or rcl then.
Good Luck with your decision - there is a ton of great advice here, keep looking around!!