Which one?  Well, it depends.  To simply suggest you always do it the same way regardless shows a complete lack of understanding about the fundamentals of marksmanship.  So unless you can guarantee that all your gunfights will be in elevators with obese aggressors, read on.

The question of sighting with with one eye or two eyes while shooting has been around for a long time. As in much of what we are doing, it is a matter of context and distance.

If you are fighting a bad guy at five feet as you explode off the x, intent on shooting him to the ground, keeping both eyes open and focusing on the threat will work fine. Try the same thing at 7 yards, shooting past an innocent, and your results will not be as good.

As most things, it depends on the problem at hand.  Like degrees of movement (from stationary to sprinting), the use of the pistol's sights (from focus on sights to focus on threat), the rate of fire (from carefully pressing the trigger to machinegun mashing it as many times as needed), and now the eye usage (from both eyes open focusing on the threat to one eye open only and focusing on the sights) - what you do and how much depends on the difficulty of the shot.

For close range gunfighting, during movement, against a torso target, both eyes open makes sense.  This type of combat is simply a slightly extended hand to hand fight.

For problems requiring greater marksmanship, and they do exist my "elevator combat specialist" friend, I teach to close the non-shooting eye (notice I did not say the non-dominant eye). This gives me greater clarity of focus on the sights or dot and a greater ability to align them properly on the distant or difficult target. It also excludes unnecessary information from distracting me from the shot at hand.

So check for yourself and I think you will find that you are far more accurate with the non-shooting eye closed.

Another issue is the dominant eye. At basic levels the dominance difference may be great. The greater the disparity, the more the need to shut off the non-dominant eye. The less the difference in disparity, the less important it is at the closer ranges. The greater the need for marksmanship, the greater the need to close off the other eye.  However, I have never met anyone with equal dominance in each eye.

At advanced levels we seek to train both sides equally as well as both eyes. Thus, I do not have a strong side or a weak side...I have a right and a left. When I am shooting in Close Range Gunfighting, I keep both eyes open and don't worry about it. As the distance increases, and subsequently the demands on my marksmanship also increases, I need the sights more, I seek them and when I see them, my body makes a determination about whether I need to close the "non-shooting" eye.

Its automatic. I don't over think it.

If the weapon is in my right hand, I sight with the right eye. If in the left hand, then sighting takes place with the left eye. And by sighting, I don't necessarily mean direct use of the sights but rather the "processing of the visual information" with the eye that is in line with the gun.

The use of the eyes, once you understand their role, is like chewing gum and walking. The more you think about it the harder it is.