The previous posts didn't address the supposed importance of eye dominance. Some believe it is of little importance, others, such as myself, believe it is at least moderately important.
If the dominant eye is closest to the pitcher when you are hitting you should see the ball better.
I believe eye dominance is important as I've seen good results with opening up the stance of those with the opposite situation; dominant eye furthest away from the pitcher.
Opening up a little or a lot keeps the dominant eye on the pitcher a lot longer in the swing and kids report seeing the ball a lot better. Just make sure you practice closing up a few thousand times before you go to the plate in a game!