My experience shooting close quarters, at sniper school, and on various three-hundred meter popup ranges is that I need to close one eye in order to accurately shoot at a target past fifty meters. Close than fifty meters and I don't even have to bring my rifle up to the accepted shooting position, at the shoulder, in order to accurately hit. I can shot from the hit or underarm position with a rifle, automatic rifle, or machine gun and hit targets that are inside of fifty meters. A high percentage? No. But at that range I have to get rounds headed in his direction before he gets rounds headed in my direction. Will this work for everyone? I can't say, and I wouldn't say. I am only sure of what works for me. Outside of fifty meters I need to bring the rifle up to my shoulder and access the sights. I might even have to take a knee to do it, I'm not sure. I don't recall if I've ever tried to hit targets past fifty meters while standing. If they were shooting at me, I'd probably do some snap-shots on the run, rather than stop to take up a good position and return fire. I learned that in my time at Bragg...when the bad guys have a bead drawn on you, seek cover first, then return fire. You may go to return fire and have a malfunction of some sort, which you probably won't live to clear if you don't seek cover first.
But I digress. With pistols, it's a whole different story. Outside of ten to fifteen meters I will absolutely access the sights, usually with both eyes open, but I will take time to aim. Misses count, but I'll never be able to miss fast enough to win a gunfight. Snap-shots might be okay initially, but aimed fire at that distance is a much better bet. Inside of ten meters, with my personally owned pistol, I can be pretty sure of getting a hit, somewhere on the bad guy, without needing to use the sights. Inside of five meters I feel confident I could do it with a pistol in each hand, if necessary.
When shooting at any kind of appreciable range, though, I will absolutely close one eye in order to shut out the noise that having both eyes open causes. It's a lot easier for me to focus with only one eye open, and I think that my scores at the ranges have been pretty consistent with this approach, which tells me it's the technique for me to use in combat as well.
Kent