I've tried both, and I tend to close one eye to sharpen the sight image and wind up having blurry vision as a result. When I started shooting bullseye pistol I wound up taking a pair of shooting glasses and using a piece of 1" wide electrical tape and put it over the eye I wasn't using, so I could keep both open, get a good sight picture, and still have the benefit of only using one eye. It's also cheap, and easy to fix if the tape peels off or you just want the tape off. Alternatively, you can get the flip-up black or white eye covers from shooter's supply places like Creedmoor and just clip them to your shooting glasses. I did this after the first season shooting bullseye because it's nice to be able to flip it up and keep the glasses on. The electrical tape option is cheap, easy, and you can vary how much of the lens is blocked. Or, if you have a pair you don't mind permanently altering you can mask off the lens you want to use and hit the other with flat black spray paint.

But blocking off the eye you're not using is the best way I've found to be able to keep both eyes open and shoot. That preserves my peripheral vision while giving me the sharpness of having only one eye looking at the target. I find I shoot better that way than closing my off eye.

I'm not sure if this would be classified as one eye or two?