As has been said, use which ever method you are most comfortable with and which you are more accurate with, during my LE career part of my duties was the department firearms instructor and armorer, I was Alphabet org trained as an instructor and attended two Armorers schools, and also instructed for a couple of other area LE agencies.
In the time I worked with allot of officers that had trouble qualifying and was able to make suggestions that helped them be better shooters, in my opinion when shooting a shotgun, open sights, or any optic without magnification it's best to keep both eyes open, everyone has a dominant eye, most right hand shooters have a dominant right eye, most left hand shooters have left dominant vision, for those who have a problem shooting with both eyes open (as someone with one eye stronger than the other), wearing a patch that covers the non dominant eye during shooting a few times usually solves the problem.
However, shooting with a scope is different, an optic with magnification increases thee distance that one can see, most rifle scopes have a set objective lens, usually set for either 50 or 100 yards, some scopes (usually variable powered scopes) have adjustable objective lenses that can be adjusted for different yardages from 15 yds. to infinity, when looking through a scope that magnifies the target image the non dominant eye is not seeing the same image, example: you are right eye dominant, you are looking through a four power scope and seeing an image four times closer than your non dominant eye which does confuse your vision, it's better to close your non dominant eye.
If you have normal vision (even if you wear corrective glasses) when you are looking at an image with both eyes open you vision is not impaired in any way, but close or cover one eye and your vision is impaired, you've lost your depth perception, when looking through a magnifying optic with one eye, your other eye doesn't see the same image in the same way if it remains open.
That's not speculation or opinion, it's natural biology.