I did a Princess cruise from Vancouver to LA. We ended up in a HA balcony room that was HUGE! Service was comparable to
DCL, in my opinion--host was friendly and room made up as soon as we left for breakfast.
I thought food on DCL was better, but my mom, who is a frequent/platinum cruiser on Princess, prefers Princess food. I find, as a vegetarian, more options on DCL and that the food tends to change on the buffet, whereas Princess, the food seemed the same ol' stuff. One difference I prefer on DCL is the how they tend to ensure you take a wipe for your hands (I've had CM nearly chase me down to ensure I've taken one, despite having taken one already

). Princess just has the Purell stands for you to use with no one there to "police" it's use. I'd say at least 80% of the people entering the buffet did NOT use the hand gel

!!
The pools seemed less crowded (but it didn't seem as warm to be out in them, so could be an itinerary thing). Definitely less kids and older population. We liked the Movies Under the Stars--comfy loungers and warm blankets with popcorn handed out. During the day, wide variety of movies played poolside. I enjoyed the games/trivia shows they had. There was an interesting talk by the cruise director and how he came to have his job--very interesting, but I tend to like talks like that. The production shows were, meh. I preferred the shows on DCL but the comedians were pretty good.
DCL definitely beats Princess in the disembarkation process, hands down! Since I was cruising with my mom, who has some crazy ridiculous platinum-like status, we were able to wait in a "special" lounge until we were cleared to disembark (supposedly, platinum cruisers get to disembark first and are escorted off). Thank goodness for that! There were people waiting all through the walkways/bars/lounges with their bags, waiting to disembark when their number was called. It was so crowded that just walking through the masses started to make me claustrophobic!
The differences on Princess definitely would't stop me from cruising with them again. They're just not DCL. And when my mom is on DCL, I have to remind her that she's not on
Princess 
. We'll likely book with them when we're ready to do AK.