Cunard has gotten much more casual the past few years. For example, jackets are no longer required at dinner. But it's still more elegant and refined than Celebrity or Princess, where many people take "formal" or "evening chic" to mean T-shirts with no holes.
To us, Princess and Celebrity uset to be pretty much the same, but Celebrity is rapidly declining with their recent changes and is trying hard to become Royal Caribbean so I'd rate Princess to be a better line. And if you're a dancer (like many Cunard cruisers), Princess generally has more and better dance venues than Celebrity, though it's very ship-dependent.