I've sailed both lines. What I like about NCL - O'Sheehan's/ Local, the thermal spa, interesting itineraries, NCL allows you to make advance dining reservations with a dining package which Royal hasnt.
I love Royal Oasis class ships including the entertainment. Our next cruise is on the Symphony. We will be going to CoCo Cay which has a dock. Great Stirrup Cay does not have a dock. Also, Royal's drink packages work on CoCo Cay whereas Norwegian's doesn't work on Harvest Caye. Bottom line, they both have pros and cons and variety is of the spice of life.