A lot will depend on your personal preferences. Do you like lots of activities to choose from, or do you plan to spend most of your time watching the scenery? (RCCL has the edge on activities, especially onboard.) Would you prefer having an assigned dining table and time every night, or would you rather have a more flexible schedule and just eat dinner whenever you feel like it? (If the latter, choose Princess.) Will you be doing a land tour of Alaska before or after your cruise? Princess has their own lodges, although both cruise lines have special dome cars on the RR. Princess may have a slightly older clientele onboard (averaging 50s instead of 40s), although that varies each sailing.
Have you met with a cruise-oriented travel agent? They may be able to help you decide which cruise line you'll be more comfortable with. Both are beautiful ships.