Let's say that you shoot three frames at a hummingbird. The first one is without flash, and you fire at 1/60th of a second. The camera sees all of the ambient light at 1/60th, and there is a lot of blur in the bird's movement.
Now, you shoot the second one with a "big" 550EX external flash set up for normal sync, and the camera is set at its maximum sync speed, i.e. 1/200th or so. The actual burst of light is much faster than 1/200th, and it hits sometime during that 1/200th shutter time. You will see much less blur in the bird's movements, and ambient light won't figure in.
Now, you shoot the third one with the 550EX set for high speed sync, and the camera is set to 1/1000th shutter. The actual light will be a short series of light bursts that are spread out in time so that one light pop will be present at any point in the shutter travel. Ambient light won't figure in.
Which one of these three will give the best results?
I vote for the second one. The single flash is about 1/10,000th of a second, and that will freeze motion better than a short series of light bursts that are spread out over 1/1000th of a second.
For a child, you should not have to shoot faster than 1/1000th or so.
---Bob Gross---