Since we went on this cruise as a result of being nagged by a friend who's both a great person and an NCL zealot, I owe it to her to compare NCL with RCI, especially since I would have blamed her for a disaster.
Honestly, the two lines are more similar than different and the choice between them comes down to price, itinerary and which set of mosquitos bothers you less.
Embark/Debark is excellent on both lines, somewhat better than Princess and worlds above Carnival.
MDR food is also good to excellent (depending on the specific meal) on both lines, with NCL a slight touch better BUT service is a very different matter with RCI way ahead.
Buffets are equal for breakfast but NCL has more and better choices for lunch and snacks, including 24 hour ice cream which is a deal sealer for my wife. Traffic flow is about the same and seating is decent to tight on both BUT NCL has more seating options including the outdoor seating at the stern.
Midrats - NCL blows RCI away. PERIOD.
Cabins - We stay in balconies on both. RCI's cabins feel bigger and more comfortable. NCLs glass door showers and removable showerheads are an big improvement over RCI but anyone over 5'8" will have their knees under their chin when using the toilet. The balconies themselves are equal except that the clear panel on NCL is preferable to us.
Bars - Spinnaker matches up to the Viking Crown and the Star Bar matches up to the Schooner BUT the Schooner stays open late and the bartenders in the Star wanted us out by midnight. Advantage RCI.
Production shows - Pretty much equally bad on both lines.