Closed bridge- helps keep the cue from wandering, more secure and controlled.
Open bridge- gives uninterupted line of sight down shaft for aid in aiming.
I use an open bridge most of the time, mostly due to the fact that thats how I learned, and it is now habit. I like the benefits of a closed bridge, but have trouble making some cut shots when using one. I adjust my bridge hand while getting down on the shot, and it kinda looks like I am tapping my fingers. I am really just making small adjustments to the placement of the bridge. Many players tap their fingers just as a nervous habit, and it has nothing really to do with shooting at all.