There are definite advantages to both eyes open, IF you can do it. What it takes is an eye dominant enough over the other to work. I don't have that. My eyes are "neck and neck" in that race. I normally shoot right eyed, because I'm right handed. I sometimes shoot with my left eye when I'm shooting around the left side of an object.
When I shoot with both eyes open, I either have to focus on my target, which is bad because I don't get any feedback from the sights to tell me where I'm hitting (can't call the shot), or I see two targets and two sets of sights. I always close my left eye, even in simunition training.
Closing one eye hasn't kept me from getting Master in two divisions in IDPA, or A class in USPSA. Its not a "must do". If you can do it, great, if you can't, don't feel like it something you have to spend all your training time on.