I just cruised with NCL on the Norwegian Dawn this spring. Previously, DH and I had always cruised on
RCCL. We loved the Dawn -- beautiful ship and crew were generally quite pleasant. Two things that really helped make the Dawn the right decision for that trip were that NCL was running a special with 3rd and 4th passengers free (just paid taxes/tips for the kids, otherwise their fare was free) and NCL's KidsCrew would take children at 2 years-old and in diapers (gave me a pager for DD's diaper changes). We LOVED their KidsCrew. However, DH and I both felt that the service and food were not as good as on RCCL.
On our previous RCCL trips (a few years back), we had found the food to be excellent and the service in the diningroom to be quite good. We loved the attention we received by having the same waitstaff at dinner every evening. On NCL, tips are automatically charged to your account and your cabin steward and waitstaff are tipped from a "tip pool". You can tip extra, if you wish, but most people probably don't do this and we really didn't experience much in the way of "outstanding" service on NCL. Also, because of the Freestyle Dining, you don't have the same waitstaff every evening and don't build the rapport with your waitstaff that we had had on RCCL trips.
We just booked at cruise for late summer next year. RCCL cost $1000 more than the NCL ship we were looking at and the difference was entirely in the cost of the kid's fares!!!! However, the RCCL ship had self-service laundry and the NCL ship did not, NCL charges extra for in-port child care and RCCL does not, and RCCL was offering free
trip insurance. Those three things make up about $600 of the difference for us. So, we'll be checking out RCCL for the first time in a few years.
IMO, for a similar price, similar ship, similar accomodations, etc... I'd go for RCCL.
Edited to add: NCL Dawn does have self-service laundry, but the ship we were looking at for next summer (Spirit, I think?) did not.