On NCL, you have the option to dine in the Main dining room for lunch on embarkation day, which eliminates the need for going to the crowded buffet with your carry-on, and hunting for a vacant table. I didn't notice that option on RCCL.
I thought that our Oceanview cabin on RCCL was a bit larger on Explorer, and they had a designated movie venue onboard along with a skating rink. My husband and I enjoyed the movies and the ice show. On most NCL ships, movies are shown in the atrium, and noise from passersby is distracting.
The food on NCL is very good.