Hi--
My family went on a Royal Caribbean cruise out of Vancouver--ages varied from 14 up to 80, which is why we were going to celebrate (there were 16 of us total). Everyone semed to enjoy the trip. We like the assigned seating times for the large family, as it gave us a time to get together and enjoy each other. Our rule was that everyone had to attend the dinner, and we ended up loving it. The teens seemed to be thrilled with the activities, and I didn't hear anyone complain the whole trip.
That said, I've also enjoyed Princess as well, and have wanted to try NCL. So, any of them might be good for you. I'd look into itenerary (i.e. whether out of Seattle or Vancouver, or one-way versus round-trip), as well as what kind of food seating you guys might prefer. NCL does not do tradiitional seating, and Princess offers mostly the flexible seating on its Alaska cruise, but you can do traditional as well. That might be a bigger deciding factor for your family.
For a big family, round-trip (inside passage) might work best for you. However, our family did the one-way and had no problems getting it all coordinated!