We did Disney to Alaska with our 14 year old. At the time, it was the best family vacation we had ever taken. Yes, I would have preferred Glacier Bay to Tracy Arm (DH and I had done a small boat tour of Tracy Arm a long time ago, but never Glacier Bay). But we still loved every minute of that cruise, and we never even considered another cruise line. Our son was still very much into the "Disney" aspects of the cruise. I think Schmoo nails it with her question of whether or not you're looking for a
Disney cruise that happens to go to Alaska, or if Alaska is the main focus. For us, at that time, it was definitely the former, and sticking with Disney was absolutely the right choice. Now, flash forward 4 years and we have another Alaska cruise booked on NCL for 2017. We never even considered Disney, because this time it's all about going to Alaska. Our son will be 19 and will have aged out of the youth programs. The Mickey aspect is not nearly as important to us this time around. On our last Disney cruise (11 night Norway/Iceland) we really didn't take advantage of the things on the ship - just a few shows here and there. The rest just didn't interest us that much or we were too tired from very long days in port. While the trip was amazing in every way it was because of the destination, not because we were on a Disney ship. The Disney service (and seeing Viking Goofy all over the ship) was a nice plus, but it didn't make that trip for us. We are really excited to try NCL for Alaska. We chose them because they:
1. Went to Glacier Bay (as does Princess, HAL and I believe Carnival (could be wrong about Carnival)
2. Offer one way itineraries from Vancouver (we've been to Seattle several times and wanted to explore Vancouver this time) to Seward to open up an additional week of land based adventure. We aren't packaged tour kind of people so we are renting a car and going our own way. Had we wanted a packaged tour, as others have said Princess and HAL have the most experience at that, though NCL does offer them.
3. We love, love, love the idea of Freestyle cruising. We are pretty much over the whole eat when and where we are told concept. I know a few other lines have started "anytime" dining, but NCL really pioneered that concept and their ships are specifically made for it. We are excited to try it.
4. We are hoping for a younger demographic on NCL vs Princess and HAL. I don't know how that will play out, but from what I've read HAL definitely wasn't for us (my son pretty much nixed that from day one) and for whatever reason Princess just didn't feel right to us, either. We are looking forward to leaving the dressier clothes at home and living in jeans and shorts for two weeks.

Dressing up for me will mean ditching the hiking boots for a pair of clogs or ballet flats.
5. We have booked an aft suite that includes the unlimited beverage plan, 4 nights of specialty dining, 250 minutes of wifi and $150 in shore excursion credits (doubt we use the last one, though) plus all of the cool suite perks. When you factor in the extras, we will probably end up paying less than we would for a standard balcony on Disney and paying for those other things separately.
We weren't necessarily looking to take a less expensive cruise, just one that seems a better fit for us at this time.
All that being said, if you choose Disney I have no doubt you will have an amazing vacation as did we four years ago. With the age of your children and just having come off of the Fantasy, they will love it. Whatever you decide, I have no doubt you will find Alaska as incredible as we did . This will be our third trip there and I'm sure it won't be the last! You can always do what we did. Give your kids a taste of Alaska on Disney and then go back later for a more immersive experience on another line or even a totally land based trip.