I prefer the single actuation as I feel I would rather get the exact moment than trust to the shotgun method of probable got it.
There is a delay between the moment of activation and the result of exposure. In some cameras with auto focus, you will get a delay, while the mechanics of exposure run through the system of focus then take the image. In some the flash must fire then you get the exposure and this has caused many a candid to fire too late. You can pre-charge the flash, but the focus delay will still get you.
In sports baseball photography there was a phenomenon known as the ball in the catcher's mitt. The shutter was pressed as the batter swung, only to have the delay not take the image until the ball had already passed the batter, either coming or going. Using a motor drive only gave you a better chance to miss the shot, but with more examples. An experienced photographer knew to take the image just before the ball got to the plate, expecting a delay in tripping the shutter. You did get a lot of worthless images, but when there was action it was on time. Single exposure shutters have the advantage of leaving you in control of the timing.
In portraits, the smile or other dramatic gesture lasts 1/2 second or less, so you must react quick enough to catch it, ideally at its peak. This is why my camera has already been focused and I am waiting for the exact moment to then fire the release. This can be done with an autofocus camera by pressing the release down partially to pass the focus relay, or even easier with a manual focus camera who doesn't have this delay.
Another example of practice makes better photos.