Another way ND filters can be used is to improve flash efficiency compared to high speed sync.
Quick Review of Sync Speed:
Sync speed is the fastest shutter speed that will still allow the entire image frame to be exposed to the flash. At a shutter speed higher than the sync speed, the rear curtain of the shutter begins to close even before the front curtain has traveled fully, so at any particular point in time while the front and rear curtain are traveling, only a portion of the image is exposed (let's call this the "window"). As a result, if flash is fired at that time, the flash beam would reach only the window portion of the image. The part that is not reached is usually seen as a dark bar along the edge of the image. For this reason, many cameras prevent you from selecting a higher shutter speed than sync speed if the camera knows that flash is being used (however, the camera can be tricked into firing anyway with the use of a radio trigger).
High Speed Sync:
High speed sync works around the natural sync speed limitation by causing the flash to fire repeatedly while the window is traveling, thus in effect allowing the entire image to be exposed to the flash. The downside of high speed sync is a drastic reduction in power. Instead of one big output, the flash releases multiple smaller outputs. The higher the shutter speed, the more drastic the reduction in power.
ND Filter vs. High Speed Sync:
Using an ND filter is a reasonable alternative to high speed sync and allows the flash to function more efficiently. To prove the greater efficiency of an ND filter, I did the following test: I compared flash ranges between high speed sync versus the equivalent range with an ND filter. I did this comparison with an ND2, ND4, and ND8 filter.
Test 1: 1/250 with ND2 filter vs. high speed sync at 1/500.
- 1/500 shutter speed @ f/2.8, ISO 200. Indicated range (displayed on the flash): 5.0 meters.
- 1/250 shutter speed @ f/2.8, ISO 200 with ND2 filter (1 stop reduction). Indicated range: 15 meters. Adjusting for a 1 stop reduction*: equivalent to 10.7 meters.
Test 2: 1/250 with ND4 filter vs. high speed sync at 1/1000.
- 1/1000 shutter speed @ f/2.8, ISO 200. Indicated range: 3.6 meters.
- 1/250 shutter speed @ f/2.8, ISO 200 with ND4 filter (2 stop reduction). Indicated range: 15 meters. Adjusting for a 2 stop reduction*: equivalent to 7.5 meters.
Test 3: 1/250 with ND4 filter vs. high speed sync at 1/2000.
- 1/2000 shutter speed @ f/4, ISO 200. Indicated range: 2.5 meters.
- 1/250 shutter speed @ f/4, ISO 200 with ND8 filter (3 stop reduction). Indicated range: 15 meters. Adjusting for a 3 stop reduction*: equivalent to 5.4 meters.
*Note: the range adjustment for a 1, 2, or 3 stop reduction is based on a division by a factor of 1.4 per f-stop. See here or http://www.photozone.de/the-guide-number-gn . Thus a 1-stop reduction would divide the range by 1.4. A 2-stop reduction would divide the range by 2. A 3-stop reduction would divide the range by 2.8.
The range with an ND filter is consistently at least double that of the range with HSS, implying at least a 2-stop advantage (i.e., 4x more available power) with the ND filter.
Conclusion: all other factors being equal, using an ND filter at the camera's sync speed will allow the flash to reach a longer range (i.e., have a higher effective output) compared to using a faster shutter speed (with equivalent exposure) with high speed sync. Specifically, the range with an ND filter is at least double the range with HSS. However, in cases where freezing action is the goal, HSS may be necessary unless flash duration is being used to freeze action.
I don't have access to other equipment such as other flashes, other bodies, or other brands, but given that HSS works similarly across manufacturers, I suspect the predicted increase in range will be similar for other equipment.
UPDATE: Neil van Niekerk did an HSS tutorial. He found a 2-stop loss from HSS (same as predicted by the experiment above).