We went on an Alaskan cruise this last July with our 9 (almost 10), 12 and 14 year old. They all had a great time. The kid's club was fantastic for our youngest. Lots of activities, attention and kids. Our two oldest didn't really enjoy the club this cruise, but they found plenty to do. My 12 year old and her father attended every single ballroom dance session and fell in love - so much so that she is now taking ballroom lessons at home. We also attended almost every line dancing class, game show and trivia. The staff was amazing.
There isn't a lot of diversity in the kid's food options, but my youngest was content with the offerings and my two older kids explored lots of new food options. They also loved being able to order room service via the television (plus all the fun non-alcoholic drinks - we had Princess Plus).
Note that the cabins are smaller on Princess than on Disney so we ended up booking an inside room across from our balcony room and my two older kids slept in there. My husband and I had access to their room. In the end, we preferred this setup as it would have been super crowded if all 5 of us were in one room.