In order for HSS to provide the multiple flash pulses from a single capacitor charge the flash's max output is automatically reduced to about 1/4 power. That might not be enough to drop a bright BG as far as you would like. From that point on the shutter speed cuts the flash output and ambient equally.
But because the ND cuts the flash output and ambient light equally right from the start, and because the flash is able to operate at full power, there's the potential for a greater ability to drop the ambient with the desired settings... i.e. the flash at full power is a closer match to the ambient/BG lighting.
IDT I actually addressed the question... how they compare for freezing motion.
HSS simply converts the flash into a constant light source like any other room/ambient light, and you use shutter speed to control the exposure and freeze motion just as you would w/o flash.
In order to freeze motion with flash the exposure settings must result in very nearly a black frame w/o the flash firing. You then need the flash to fire with a T.1 time fast enough to freeze the motion. The ND helps in creating the dark exposure.
With a traditional studio flash/strobe the ND additionally helps by allowing the strobe to fire nearer max output where it's T.1 time is faster, but typically not fast enough to freeze high speed motion.
With modern IGBT controlled flashes/strobes the T.1 time decreases as the power is reduced, and they can reach speeds much faster than other types. However, in this case the ND hurts because it also requires the flash to operate at a higher power and slower T.1 times.