Normal flash sync will always win that contest. It must do, because with HSS, no matter what, at least some of the light is simply wasted as it falls on the closed shutter curtains. And at high shutter speeds, almost all of it is lost in this way. In round figures, just by using HSS at a fraction above the normal x-sync ceiling, you'll lose at least two stops of effective flash exposure, more likely three, and that loss rises pro-rata as shutter speed is increased. Lots of variables though - camera shutter cycle time, flash output in HSS mode, and how accurately those two factors are aligned to minimise wastage.
Anyway, I just tried it, using the OP's settings, though I couldn't get the ambient exposure to the right level at iso100, so used iso400 (and that's despite having over 800w of fluorescent light only 2ft from the subject!). Darkened studio, with no ambient light on the foreground, and no flash contaminating the background.
Edit: Canon 7D and 580EX gun.
1/125sec at f/11, iso400. Correct ambient exposure on the background, and correct on the foreground with flash at 1/32nd power.
1/4000sec at f/2 iso400. In HSS mode, the foreground flash exposure matched the background at 1/16th power.
That's an effective difference of six stops which shows that HSS is actually pretty useless for freezing action, as by the time you've got the shutter speed up high enough for that, there's precious little flash power left, and with a lot of action subjects the longer shooting distances make things much worse. The only solution to that is to gang multiple guns, as Dave Black does in this video clip, using an eight-gun rig. That seems to work
What HSS is really good for, is fill-in flash in bright daylight when the shutter speed inevitably has to rise above x-sync. Portraits perhaps, at close-ish range, but not trying to over-power the sun - there's rarely enough poke for that. And in the same way, it works well when shooting at lower f/numbers for shallow DoF.
