I think that over the last twenty years there has been a shift towards the open bridge even among American and Pinoy players (the European players, with their snooker backgrounds, have been utilizing the open bridge extensively from the beginning). In situations that don't call for a huge amount of power or spin, a good open bridge is more than secure enough (if the player's stroke is solid), and it allows an unimpeded sight line.
As to how one decides which bridge to use, the greatest factor will be whether the shot requires a significant amount of force and spin, in which case most players will opt for the closed bridge. As one's stroke develops, however, one finds that even draw strokes and other power strokes can be executed comfortably with an open bridge. Thus, a pool player's selection of bridges, as he moves from beginner to intermediate to accomplished player, often follows a path similar to that of a martial artist, whose belt passes from white to black and back to white. The beginner will use the open bridge wherever possible, the intermediate and somewhat advanced players tend to use the closed bridge wherever possible, and as they move toward expert status they begin to gravitate back to increased use of the open bridge.
The more you play and develop in the game, the more the decision of which bridge to use will become an unconscious one. You'll just automatically make the bridge that is required and that feels right.
I agree with the meat of this post. Essentially, that very last paragraph nails it -- at high levels of play, the choice of bridge tends to (and *should*) be an unconscious decision.
However the bolded part is not always true. Many of the top pros shoot almost exclusively with a closed bridge -- e.g. Dennis Hatch, Mika Immonen, and in times past, e.g. Mike Sigel, Steve Mizerak (Steve also used the closed bridge when he played his challenge matches on the snooker table against Steve Davis).
Some cite the unobstructed sight line as the reason why they prefer the open bridge. For others, the mind's natural ability to unconsciously "stitch" images together makes the overlapping finger of the closed bridge completely disappear from view, making the unobstructed sight line a moot issue.
In any case, the choice of bridge should almost always be a subconscious decision. You shouldn't be focusing on your bridge anyway -- you have that shot in front of you that you *should* be directing your attention to.
I find that when I'm "lazily" practicing -- i.e. slamming balls home into the pockets, to loosen my arm -- I tend to use the open bridge *a lot*. It's more a laziness issue -- I'm more interested in the sensations I'm getting in my cue delivery arm (e.g. making sure the cue delivery is straight), than in my bridge. So I tend to slap my hand down on the table like a frozen burger patty, and in the same motion as bringing the cue down on top of it, pinch the thumb against the index knuckle to form the "V" channel that the cue rides on. It's just a "quickness" thing.
But in competition or matches that matter, I'll buckle down more, and use the closed bridge a lot more often.
It's funny, I don't notice it, until someone points it out to me, and asks me "why do you use the open bridge during practice, but then close it when the match begins?" :shrug:
-Sean