Considering the fact that the average flash is in thousands of a second, neither high nor lower powered flashes freeze action greatly more than the other, though at full power, flashes will have a shorter duration than when at lower power levels.
However, an "action shot" taken with a flash that cycled at 1/3,000th of a second vs 1/15,000th of a second will give you the same level of frozen action effect. At these levels, shutter speed will have more to do with reducing blur than flash speed.
Strobes used to freeze the jumping action here. We can see the body well in focus, but the legs are blurred with this picture taken at 1/200th (lighting was 2 Nikon SB-600s set to 1/4 power):
Yet when ISO and shutter speeds are raised to ISO 3200 and 1/500th, this blurring completely disappears as displayed by this much more aggressive and faster spinning jump kick perfectly captured without any motion blur (NO lighting beyond ambient was used in this picture!):
There are times to use flash to freeze a moment, but faster moving objects will still have blur until you raise shutter speeds. That is where having a camera with a higher sync speed comes in handy unless your ambient is very low (or as suggested, your apertures are VERY small and strobes strong enough to overpower the conditions).
2 ways to do the same thing.
