jlmkey, we've sailed on Princess, Royal, Costa, Carnival, HAL, and NCL. Princess is my favorite, but that is because their product offers my tastes the best fit. Each cruise line has it's own character. My impressions are: Princess is elegant without being snobby. Royal is more family oriented with more "glitz". Costa is totally family oriented with an Italian flare. Carnival is family oriented with an emphasis on "fun". HAL is elegant and more subdued. NCL is family oriented with a laid back atmosphere.
Princess ships are immaculate, the service is impeccable, and the food is good to great. Costa's ships are immaculate, the service is wonderful and the food is good to great. And so on with the list.
SonnyV has been on over 50 cruises with Royal, f-mattox has been on about that with Princess. I've been on 9 Princess cruises and 3 Royal cruises. They're just different experiences and I personally prefer Princess. I'm not going to use the rock wall, the ice skating rink, or the florider, so I'm not going to pay more for a comparable itinerary. If Royal had an itinerary that I wanted and at a price I thought was reasonable, I'd book Royal.
I know this doesn't sound like I answered your question, but I'm trying. They're both great cruise lines and I don't think you'd be disappointed in Princess at all. However, I don't think I'd call it a step up. Best wishes!