Bob's right, snooker players are the highest-paid, and they all use open bridges on all shots, including power shots. Ronnie O'Sullivan, since taking an interest in pool, has begun using a closed bridge on the snooker table from time to time, but when he does, the commentators make a big deal out of it, because it's not done in snooker.
Anyway, there's only one real advantage I can think of from one bridge to another, and that's sighting. If you use the visual line of the cue to sight your shot (I'm not sure everyone does), then that line is broken up and partly obscured with a closed bridge, and entirely visible and unbroken with an open bridge. How much difference this makes is debatable.
As far as having better power or control one way or the other, it shouldn't make a difference. If you're cueing straight and smooth, the bridge should be totally transparent, as long as it's placed in the right spot, and it doesn't move. The only way I can see any difference is if you have a tendency to lift the cue up off your open bridge, then the closed bridge would help. But if you're doing that, there's something wrong with your stroke, and your power and accuracy are going to be inhibited until you get that fixed, no matter what bridge you use.
-Andrew