We have cruise both cruise lines and find them pretty equal. Some aspect may be better one but is set by something better on other. Royal ships definitely have more 'fun' items - rock wall, ice skating, wave rider. Last trip on RC (Mariner of the Seas) we found the elevators challenging and ship seemed crowded. Princess had a wider range of intineraries but RC is catching up.
Dinning option is definitely a personl choice. We perfer traditional early because we get to know the servers and enjoy the personal service. Also we like the early seating to have the rest of the evening to do other things and in our home life we usually eat about 6pm anyway so we keep in the routine. But if you are use to eating late at home late seating might appeal to you more. We have tried all the other options - anytime and also traditional late. But no problem going to the specialty resturant. Be extra hungry because when we have gone to those resturants the food is overwhelming. We usually inform our server when we won't be showing up for our regular dinner just as a courtesy to them. We have booked just table for 4 (our family) and also had seating with others. We have had some interesting table partners and guess the best to say is we have great stories to share about our vacation dinning experience.
Great that the cruise lines give options for everyone.