We've sailed HAL and Celebrity to Alaska but not Princess. Hard pressed to say one was better than the other. Both were great. I have one "problem" with Celebrity however when booking future cruises. They don't go to Glacier Bay. Although Hubbard glacier was beautiful, in future Alaskan cruises Glacier Bay will be a must for us. We've never sailed Princess but they do go to Glacier Bay so I would consider them in the future.