T-bone, Princess has two advantages, IMO, over the other 2 cruise lines you have already sailed with: 1) more experience in Alaska (they've been there longer) and 2) Personal Choice dining. We did the Personal Choice on a s. Carib. Princess cruise last year and really enjoyed it. A couple tips, if you have opted for it: go to the most out-of-the way dining room that participates in Personal Choice, as it will be less busy than the one(s) closer to the action. And be prepared to wait unless you eat early (before 6:15) or late (after 9). Alaska cruising can make for some long days, so Personal Choice would be my pick there too - gives you more flexibility about how long you can stay ashore in the ports.
Another tip - if you are not staying overnight in Anchorage after your cruise (or doing a land tour w/ Princess), and if you have booked your air through Princess, you may want to inquire very soon about "air deviation", which allows you to request specific flights. I've noticed that lots of flights leaving Anchorage for the lower 48 leave in the middle of the night (1 or 2 AM), which hardly makes for a restful experience!