I'm sure this has been answered by some of the more knowledgeable people down below, but I'll put in my two cents here.
The answer to this generally depends on use case.
If you're looking to not disturb your significant other while they're sleeping, then yes, the closed-backs offer superior noise isolation and will let them sleep in peace. I've found that open-backs, even when not played loudly, can leak out quite a bit of sound even when played quietly (and I tend to listen at relatively soft volumes). They also have the advantage of having better bass response due to the fact that the sound is contained within the earcups.
However, the downside is that the sound bouncing around in the earcups can cause unwanted distortion of the driver and can also muddy frequencies produced by the headphone. Also, they trap heat much more easily, tend to be heavier, and definitely suffer from the "in-your-skull" sound that is a (legitimate) criticism of headphone listening.
If you're in an environment where you won't disturb others (or the other people don't care), then open-backs offer superior soundstage, a much more natural sound, tend to be lighter, and trap way less heat. With the majority of my open-back headphones, I can keep them on for long periods of time and not really notice any discomfort due to heat.
That being said, the drawback is that they not only leak out sound to everyone around you (basically, don't use these if you want a private session with some 'adult' material), they also let all sound in. Which means that you'll hear everything around you at the same time, making them generally unsuitable for outside use. However, some people (like me) find this trait to actually be beneficial, as I maintain awareness of when cars pass by when I walk. Also, they can have less bass due to the fact that none of the sound bounces back.
One design is not inherently "better" than the other. The really important thing is do they sound good to you? If the answer is yes, who cares what their design is?