When cruising Alaska, it's really tough to beat Holland America. They've been doing it longer than everyone else and have the biggest presence. We spent 2 weeks with them doing a cruisetour and they own all their own hotels and lodges, so the quality is very good throughout.
Princess has the second biggest presence in Alaska and are very good as well.
Celebrity doesn't have as big a presence, but they are definitely very good.
When cruising, our personal favorite is Celebrity because they are more upscale, food is outstanding, ships are very nice, and the service is wonderful. However, they do tend to attract an older crowd, so their cruises can be more sedate than Princess.
Holland America also attracts an older crowd.
If you don't mind an older crowd, of the two choices you're considering, I would suggest Celebrity. If you want a younger crowd, then I would suggest Princess.
However, as was mentioned, one of the biggest considerations may be the itinerary. For example, some go to the glaciers, some do not. So if you definitely want to see one of the two major glaciers (Glacier Bay or Hubbard Glacier), then the itinerary may make the decision for you.
Also, if you have the time and money you may want to look at a cruisetour instead of just a cruise. It's an awesome way to get into the interior of Alaska so you can really see all that it has to offer.
But no matter what you decide, you'll have a wonderful time because Alaska is amazing and definitely a cruise you have to do at least once in your life.