The difference is once you start using it in a playback audio system it changes. Its because you now have your digital source hooked up to an amplifier used to drive loudspeakers. Everything gets amplified. Its mostly due to the quality of gear out right now. Bryston and other manufactures are building really sensitive high energy playback systems. These systems pick everything up now coming off the source. Literally everything and that includes harddrive quality and their power supplies.
I really don't know why the bass was affected, other than something in the lousy Omega power supply crapping out. 
So now you are onto something...
As per my second post here, its not the cable that makes the difference but the parts on either end... such as the usb signal sender and recievers.... the quality of the disk drive power supply... the quality of the sender and reciever software... the noise rejection/amplification that sender and reciever have.
In my opinon USB HD is the WORST interface for using in this application because there is no standard for USB enabled components such as disk drives.... they are all consumer based products... so they have no mandate to be they best the can relative to an audio application.
So if a crappy sender/receiver unit in the disk drive has high levels of noise on it (and also remember USB has POWER PLUS SIGNAL down it), then that may work fine connected to a computer but will cause issues in audio applications.
Use the USB stick as a benchmark... and now you will need to do SQ comparisons between different hard drives enclosers.
And then you have the gotcha... self powered or powered hard drive enclosers.
I think Bryston should publish a recommended or "certified" list of HD enclosures that have not caused SQ issues in their opinion... else someone will buy the cheapest one out there and get SQ issues.
Peter