After reading your post, it sounds like you are looking at cost vs the experience. I have cruised with both lines and can answer a couple of questions:
Based on my experience with the two lines I can tell you that I have never seen a Princess excursion to Alaska discounted. Royal has discounted some excursions on my itinerary but nothing that I was interesting in. Also, the discount was not that significant. If you are interested in a particular excursion I can check my itinerary and see if a discount is listed.
Food is subjective so I won't comment on that. Besides, we are light eaters and usually go to the buffet -- we usually manage to find something and have never gone away hungry.
Yes, Princess does have more Alaska based activities and Alaska themed food. I suggest that you go to the Princess.com homepage, scroll down to where it mentions Alaska and click on that entry --- you will find Alaska specific information that will be of value in helping you decide which line to take.
Alaska has something for everyone and each line does it differently. If $$$ matter more too you then go with that. If you are looking for the Alaska experience, you might want to go with Princess.
Good luck to you.