I've cruised on both the Destiny and the Triumph over Christmas with my sons.
The kids will have a great time, because there will be TONS of other kids onboard in the various age groups. It will take effort for them NOT to meet others.
However, the shortcoming on these ships, is the lack of dedicated teen areas. There is no teen disco, so the teens basically end up "taking over " the disco until later in the night, when they may be asked to leave.
This does leave them sort of looking for somewhere to hang out. Often they end up congregating along the boulevard outside the disco, or the pizza bar, or arcade.
Even with organized activities lacking, I don't think the older ones will have any problems with having a good time. Just have them check the Carnival Capers the first day on the ship, and be sure to have them attend the first onboard get togethers for their respective age groups.