The biggest differences between closed and open headphones are 1 the isolation from ambient noises with closed headphones (also the other way around: the outside world doesn’t hear the sounds the headphone is producing) and 2 the better spatial sound with open headphones. Semi-open headphones are basically a mix of these both acoustic principles, combining both advantages.  
Mechanically open headphones have an advantage compared to closed headphones: the air-volume within the headphone housing dampens the vibrations of the membrane; with an open headphone there is pressure compensation due to the open housing, which influences the impulse consistency. The greater dampening of the membrane also decreases the danger of uncontrolled vibrations.  
The pressure, which emerges from the closed housing (with closed headphones), causing the membrane to not vibrate maximally can also result in bad or insufficient reproduction of lower frequencies. Some of this problem can be solved by a ventilated housing, like for instance with the DT 770 PRO. The pressure is being compensated by the ventilation and the membrane can vibrate freely optimizing, or sometimes even linearizing the bass response.  
The choice of headphone on basis of the its sound, of course depend on what we want to listen to (using the headphone). For instance for classic or jazz, where bass is soft, but the impulse consistency is very important, an open headphone is the perfect choice. For pop or rock music a semi-open or closed headphone is preferred. At the end of the story the preferred acoustic principle depends on the application (where do we want to use the headphone?). Is the headphone being used in a quiet environment (for instance a music studio), to mix or listen to music a decision can be made according to personal. In case the headphone will be used as monitor by musicians during recordings, a closed headphone is required, isolating from ambient noise and the other way around (to make sure sound produced by the headphone is not being picked-up by the mics).