I always shoot both eyes open, this allows you to maintain constant sight on your target and is good practice for deer.
With both eyes open when I release I maintain constant sight which in hunting is vital as a lot of people will throw down their bow hand to see where they hit or to watch the deer run. With both eyes open you are aiming with your dominate eye and seeing where you hit with your other eye. This helps me follow through.
If you close your eye on the release you may jerk your bow hand and you may not hit where you were looking (not following through). But it's all a manner of comfort, if you are accurate shooting one eye open, then shoot one eye open. If not I would recommend trying both eyes open.