While I generally say at that age they will have just as much fun on Royal caribbean's mega ships (Oasis, or Freedom) - there are plenty of things for teens to do on Disney - including sepaerate teen programs for ages 13-14 and 15-17.
They have huge teens-only areas on Dream. But some of the other daily activities they may find more youth oriented.
It is a safe bet, but so is RCL. Carnival Dream would be good, too.
Just avoid smaller and older ships, especially on longer itineraries,