We did a 7 day northbound cruise to Alaska on Princess sailing from Vancouver with our two daughters and my husband's parents. At the time of the cruise my daughters were 10 and almost 4. The only cruise that my husband, the kids and I had been on prior to this was Disney. All three generations were very happy with Princess. It was the first time that my daughters had ever gone to a kids club and they loved it. Summer vacation had just started (end of June) and, if I remember correctly, there were something like 150 or 200 kids aboard. The kids program was great - they had Alaskan themed activities and when we sailed in Glacier Bay there was a park ranger in the kids club to teach them about glaciers at a level that they could understand. Our ports of call were Ketchikan, Juneau and Skagway and we did a 5 day land tour afterward that went as far north as Fairbanks. We loved the Alaskan cruise!
Since then we have also sailed on Holland America in the Caribbean, Princess in the Baltics and this summer we are going on Celebrity in the Mediterranean. Of the ships that we have been on my kids say that they prefer Princess. I know I may be in the minority but I honestly wouldn't go on a Disney cruise were the ports of call are more important to me than the ship.
I have photos and a description of what we did with the kids in Alaska on my travel blog and you are welcome to have a look if you like. You can find it at Gone with the Family
I would be happy to answer any questions you have about our cruise to Alaska or our experience on Princess.