welcome to Cruise-Chat.com.
For your information, I have created a shortcut to this thread in the NCL Corporation forum and deleted your identical posting there, so whoever replies to your posting will do so in this thread here.
There's a huge difference between the "Radiance of the Seas" and "Norwegian Majesty". The latter one is much smaller (less than half the size) and was originally built for short cruises, resulting in inside accommodations starting at 118 square feet, according to my sources.
In a way Royal Caribbean is a little bit more formal than NCL, but with only two formal nights per week, you can easily enjoy the buffet up in the Windjammer Cafe on those nights if you would prefer not to dress up.
On NCL, the formal evenings are toally voluntary, and because there is an open-sitting policy you decide where, when and with whom to dine every day. If this is important to you, I would suggest NCL. My experience has also been that NCL's food was somewhat better than on RCI, but that's always a matter of taste, of course.
However, IMHO "Radiance of the Seas" and her sister ships are among the most beautiful ships in the standard segment of the cruise market. They offer far more choices than "Norwegian Majesty", but for you the question has to be whether you need all this or whether you would rather prefer a smaller, more intimate ship.
In the North American cruise market, the trend has been going towards larger and larger ships, and many people think the larger the ship, the better the experience. I'm not a fan of that theory. While there are excellent large ships, there are also wonderful smaller, older ships (I wouldn't call "Norwegian Majesty" older, by the way). If you don't care for rock-climbing and multi-story atriums, you can have a great time on smaller ships, as well.
I hope this has helped you somwhat. I'm sure others will gladly add their opinions.