I just came back from a Princess cruise, not to Alaska though.
I will say that I have been on most cruise lines (RC, Norwegian, Disney, Holland America) and Princess was my least favorite. They just don't run it all that well. The app is glitchy, the website is not at all user friendly, and the onboard programs are mediocre.
I can't vouch for Viking, but I would go with them. They definitely have a better reputation.