Hoping for folks who know the definitive answers; I have my own guesses, but that's all they are.
IMO the only folks who would know the definitive answers are those who have carefully compared a variety of recent generation drives from different manufacturers, some of which utilize wall wart power supplies and some of which utilize power from the USB bus, and have compared them using an Oppo BDP-95 or another similar Oppo player. In other words, just about nobody.
IF any of the alternatives you described make any difference, IMO it would be the result of coupling of electrical noise from the drive and/or its cable and/or its power supply to unrelated circuit points within the BDP-95, and possibly to points elsewhere in the system. And/or effects within the BDP-95 that may result from the fluctuating current drawn from it by the drive, in the case of a bus powered drive.
Noise effects don't have a great deal of predictability. And I see no reason to expect much if any consistency between experiences that may be reported with computer setups and what can be expected with your Oppo.
Personally, I'd just follow the advice RW offered in his last paragraph.
Regards,
-- Al