Basically - do they rather go to WDW, or prefer Universal or 6 flags? If they are not into Disney, they might have a pre conceived idea and not like it thinking it's not 'cool' or too 'kiddie'. In that case, then other options might be better like RCL.
If they enjoy WDW, and/or have an open mind, they'll surely have a blast. If they 14-17 they'll go to Vibe. 11-14 can go to Edge. Both clubs set up lots of activities to do on board, around the whole ship. They have a pool party, or take over the arcade (and it would be free during this time), etc. There's also teen only activities. The older ones even have their own private section in
Castaway Cay.
At 11, they can still go to Oceaneer's club, which is a secured and supervised environment. It depends on the maturity level. Otherwise, Edge is the place. At 14, they are in the border line between Edge and Vibe. They can go to either one, but again, it depends on the maturity level. If they want to be together, then Edge would be the place to go. Note that there are some planned activities that are combined like Gender Wars - but Edge competes with Vibe for example.
If they feel 'forced' going into a
Disney cruise, they'll feel bad initially. On longer cruises, this is usually not a problem as within a couple of days, they would adjust. If you are contemplating a 3n or 4n, then it could be an issue as they would not 'adjust' in time...