NCL doesn't use the work "Formal" anymore when describing these nights, instead they call it "Dress Up or Not Nights".
NCL very recently changed their dress codes for all their restaurants. Nice "Jeans" are allowed now, except at one of the main restaurants.
Resort Casual attire, slacks and a collared shirt, even at the one restaurant that doesn't allow jeans, is always appropriate on NCL ships.
It's been my experence that less than 25% dress up semi-formally, ties and sport jackets on "Dress Up Night", less than 5% really dress up formally, meaning dinner jackets or tuxedos.
If you prefer to dress up to the nines, it's okay to pack and wear your best clothes. That's what "Dress Up Night" is all about. But my main point is, you don't have to if you don't wish to. And now, you don't have to pack slacks either, jeans are okay to, as long as you're willing to not dine at that one restaurant.
From NCL's FAQ:
How should I dress for dinner?
Freestyle Cruising gives you the freedom to dress as you please – morning, noon and night.
Casual attire is perfect for all restaurants during the day -- Khakis, skirts, jeans, casual tops, shorts or whatever. Swimwear with a cover-up is fine at the buffet and outdoor restaurant.
For dinner, collared shirts and pants or nice jeans work for guys. Slacks or jeans, dresses, skirts and tops are perfect for women. But if you want to dress up and add a little glamour when you dine out, that’s OK too – we’ve reserved one restaurant each night just for that.
For kids 12 and under, nice shorts are appropriate in all restaurants at all times.