We cruise NCL a lot and also enjoy Royal Caribbean for different reasons. I'm perfectly happy to do either and will be on Odyssey of the Seas later in February. We're not foodies and find good food on either line. Probably what steers us to NCL more often is the perks. We're booked for the Prima early next year and am interested to see what it's like as it's smaller than the newer ships.
NCL: We love the Freestyle aspect where you don't have to reserve the regular dining rooms. We like the beverage/dining package perks where you just pay the gratuities for them, also the loyalty program perks (we get 2 specialty dinners & more for being Platinum). I really enjoy the newer large ships which have great entertainment and the Waterfront. Cons: the cabins are a little smaller and also the balcony. You can bring wine/champagne but will pay a $15 corkage fee for each. No other beverages are allowed unless needed for medical devices or for baby formula.
Royal: I really like some of the layouts including the Promenade, Boardwalk, Central Park, skating rinks. There are also more cabin categories so you can sometimes get a window with an inside cabin or a balcony overlooking a boardwalk/park. I like that the price seems to be better in some cases. Cons: Drink packages are really expensive and it doesn't seem like the 10 drink coupons are available now. I don't like that you have to reserve dining even with My Time.