My twins, now 15, have sailed on Princess with us 4 times and love it every time. However, they have each other and also enjoy swimming, ping pong, etc.
Be aware that the kid's programs vary greatly on Princess ships. We were on the Western Carribean on the Grand and it was fantastic! Lots of daily planned chaperoned activities in the teen center, a good teen staff, and a fair number of teens despite that it was mid year. During school break times, there are many kids onboard esp the bigger ships and the programs will likewise be active and you will rarely see your kids, they will have so much fun.
On the Regal, there is not "really" a teen program (one small room is provided for all kids 3-17, your teens won't be caught dead near it lol) and they would have to entertain themselves, likewise the Royal and Tahitian.
The Sun class ships have a small teen center but on our trip it was rarely open. A schedule of events, delivered the first day, didn't happen. They still had a great time, because kids just need each other, some music, a few games and a pool to have a great time. Hope that helped.....