HSS flash has advantage of allowing flash fill with a fast shutter and a wide aperture in bright sun. This is its purpose. Its purpose is NOT speed, continuous light has no speed capability at all.
HSS flash power also can be a disadvantage. It is continuous light at much lower power level. It is also decimated by fast shutter speed (like in sunlight), but aperture can compensate that with Equivalent Exposures. But continuous light has no motion stopping ability like flash does, just like sunlight in that regard. And basically, its maximum power level is around 2.3 stops less power than regular flash mode.
Is it actually 2.3 stops loss? Here are four ways to verify it.
Guide Numbers from SB-700 user manual, 24 mm zoom ISO 100, Standard pattern, DX mode
Page H-25, Auto FP HSS, DX Guide Number 42 (f/4.2 at ten feet)
This HSS Guide Number from user manual is specified for 1/500 second shutter, but it also applies for any faster shutter speed if aperture is opened for same Equivalent Exposure (see above).
Five HSS flashes ganged as one, is GN 42 x sqrt(5) = GN 93.9 (f/9.4 at ten feet)
Page H-24, Regular flash mode, DX Guide Number 91.9 (f/9.2 at ten feet), which is only 0.06 stops less than five HSS units, and 2.3 stops more than one HSS flash.
52 feet - For ANY shutter speed not exceeding maximum shutter sync speed (full power)
22 feet - 1/320 second (continuous HSS mode kicks in above 1/250 second - with reduced power)
20 feet - 1/400 second
14 feet - 1/800 second
10 feet - 1/1600 second
7.0 feet - 1/3200 second (shutter speed decimates continuous light)
4.9 feet - 1/6400 second
Again, all at f/4, which are NOT equivalent exposures (but all HSS equivalent exposures are equal range).
Inverse Square Law says 1.414x distance is one stop falloff.
But at the HSS shift point above, the ratio of 52 feet changing to 22 feet on the SB-800 LCD computes 2.48 stops loss (some round off in the numbers shown). Note that HSS mode works same as continuous sunlight — each faster shutter stop is half as bright (Unless also equivalently compensated by a one stop aperture change). For flash, double power is 1.4x distance range. 14 feet is one stop more than 10 feet, and 20 feet is one stop more than 14 feet. Very important to realize that we did not compensate by opening aperture one stop each step, to create the customary equivalent exposures we deal with continuous light. People are surprised that the HSS flash falls off this way with shutter speed, because they are used to regular flash which is not affected by shutter speed. But HSS is not regular flash, and the sun and other continuous lights are decimated the same by shutter speed, in exactly the same way, so no reason to get excited.
A second set of numbers, at ISO 800 and 105 mm zoom, and same 1/250 second Auto FP mode at f/4:
The first value is limited in the display at 66+ feet. But this is from Guide Number, which for ISO 800, computes GN 184 x 2.8 / f4 = 129 feet.
66+ feet (which is 129 feet) — For ANY shutter speed not exceeding maximum shutter sync speed (full power)
56 feet - 1/320 second (continuous HSS mode kicks in above 1/250 second - with reduced power)
50 feet - 1/400 second
35 feet - 1/800 second
25 feet - 1/1600 second
18 feet - 1/3200 second (shutter speed decimates continuous light)
12 feet - 1/6400 second
Again, all at f/4, which are NOT equivalent exposures (but all HSS equivalent exposures are equal range).
A -1 EV stop of Flash Compensation (for fill) increases distance range by 41%, in either regular or HSS mode.
These methods all introduce an additional 1/3 stop shutter speed increase, as the only way to enable HSS mode, which are not quite equal situations. But 2.3 stops is the ballpark loss, about 20% power level.
Pictures below show a garage door, looking west at 11:20 AM, in partial shade from a roof shadow at top, and a tree shadow lower. Unfortunately some minor clouds, some minor variance, but I tried. The fill flash is illuminating the dark shadow on the garage door (concept works same as a dark shadow on a human face). Nikon D300 in 1/250 second Auto FP mode with hot shoe SB-800. ISO 200 and Center metering, Aperture priority. 24-70 mm lens at 24 mm. Subject distance (garage door) was carefully measured to be at 12 feet (3.66 meters), which is about the limit for SB-800 HSS fill flash to help much.
So, is HSS fill flash usable in bright sun? Yes, for the purpose of a wider aperture. Is it powerful? No. And the regular speedlight is not so strong either (not at the necessary f/16). So perhaps HSS mode may not be optimum power for fill at 12 feet, but we still get considerable helpful flash fill, often usable for f/2.8 in bright sun if desired (within these range limits).
Note: I gotta say, generally, the ONLY goal of any of this HSS flash business is just to be able to use fill flash in bright sun, at wide apertures like f/2.8, if we crave that. Otherwise, HSS flash is rather weak and its range is limited. It is the full opposite of a fast flash. It conceivably could allow flash with fast shutter for fast action in sun, but the range may be too short for action. IMO, we'd be dumb to use HSS mode indoors, where regular flash will run circles around it. But... HSS can allow fast shutter so we can use f/2.8 in bright sun.