The one way in which I can envision a USB cable connecting an external hard drive to a computer could make an audible difference is by affecting the amount of RFI that may be radiated from the cable into the audio system. Like most digital signals, USB signals contain significant energy at RF frequencies, as well as carrying some amount of random noise that is at RF frequencies. In Ozzy's case, though, the distance between the cable and the audio system would seem to make that effect very unlikely to be significant.
If we were discussing a USB cable connecting the computer to a DAC, though, the story would be different IMO. In addition to RFI radiation there would be the possibility of effects on jitter, as a result of noise being conducted into the DAC by the cable; ground loop effects between the computer and DAC; and effects of the cable on waveform integrity. All of those factors could conceivably differ depending on the particular cable that is being used. Their significance would be dependent on the design of the DAC, including its jitter rejection capability, and the extent to which any noise might be able to bypass the jitter rejection circuitry.
If in fact those differences were to exist in a particular system, however, IMO that would absolutely NOT mean that a more expensive cable will necessarily outperform a less expensive cable. Assuming reasonably decent cable quality, performance would depend on the happenstance of the interaction between the characteristics of the cable and those of the system and the physical setup. Which I would expect, in turn, to be essentially unpredictable.
Regards,
-- Al