For starters, the 1DX does not appear to have unlimited sync. Pg. 195 of the manual states the max x-sync speed is 1/250 (maybe as low as 1/125, though I would expect higher with the Bees or Einstein). You may be referencing unlimited sync with Canon branded speedlites, which work differently than studio lights.
Furthermore, even if the shutter speed was 1/1000; the flash duration could be longer. If the duration is longer, then the shorter shutter will "close" before all of the flash energy exposes the sensor, thereby reducing the effective power of the flash. The flash duration of a B800 is 1/1100s t.1 at full power, and gets longer as power is reduced. B1600's start even longer.
On the other hand, with a flash duration faster than 1/1000, the flash will end up doing the work of action stopping, making the shutter speed unimportant (at least until you reach the point of letting ambient in). So a 1/4000 flash duration would look the same at 1/100 as it would at 1/1000 (again, assuming no ambient pollution). You can roughly estimate the t.1 times to freeze motion the same as an equivilent shutter speed. Einstein has a (t.1) flash duration of about 1/580s at full, but gets faster as you reduce power. At 320Ws in action mode, the flash duration is almost twice as fast as the B800 at 320Ws.
I would highly recommend the Einstein over the Bee for most things anyway, but this is the ideal environment for Einstein.
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