No simple answer. One thing in my case I would always lean towards more days on a cruise.
How the 14 of you want to cruise plays a major roll. If you all want to get together for dinner each night then traditional might be better. At least everyone knows where and when dinner is. Getting all 14 to decide where in when each day with so many choices on the Dawn is like hearding cats. A single table for 14 on either ship will be a challange. You can make reservations on the Dawn in the main dining room for a few nights for the gang but it must be before 6:00 or after 8:30
On the other hand if you want to have a great deal of flexibility and not worry about when you get back onboard then the Dawn is the answer. You can mix and match who eats together, when you eat, where you eat.
You can join the kids for an early dinner, send them off to kids club, and have a wonderful adult dinner at the Bistro or Cagney's.
As far as accomadations on the Dawn. Lots of options but it depends on the mix of adults and kids needing to room together and how fat your wallet is.
You can get 7 in the 5000 sf Garden Villa with 3 bedrooms and 3 full bathrooms for the bargain price of ~$30K
A little more pratical an AB Penthouse beautiful master suite with a bathroom to die for and a kids room and second bathroom that sleeps 3
I would avoid any cabin for 4 except an AF mini. Keep in mind that room offers two twins that can be made up as a queen and a double sofa bed - no pullman.
The regular inside or outside cabins made up for 4 are two crowded for me.