It's a loaded question for sure! Keep in mind that a USB DACs use a different protocol than a USB HDD so it's a different beast. For example, A USB HDD uses a reliable "bulk transfer" vs an unreliable "ischronous transfer", so you can always be assured that the bulk transfers will safely deliver the data or that a fault is logged otherwise.
With that said, there's no advantage of using an aftermarket cable for bus-powered or wall-warted USB hard disk drives in terms of transferring the data reliably. The self-powered USB drive will probably leak noise from the wall-wart power supply, this won't impact the data and as stated before the data isn't influenced by jitter or noise until it hits the sound card. If the wall-wart is noisy, then it might leak to any device that shares it's electrical connections either via the USB cable or power cable, but there are a number of factors that can influence that. Luckily it's a pretty easy test to see if your wall-warted USB drive is adding noise to the system since the BDP-1 comes with a thumbdrive and it's easy to copy the same song to both drives and compare (with wallwart plugged in vs unplugged).
The ischronous transfers used by synchronous USB DACs is at the heart of the issues for jitter for several reasons: usb utilization, chipset jitter, and if the cable influences jitter or is susceptible to noise. Asynchronous and Adaptive DACs re-clock the audio stream but the transfer is still unreliable where several bytes could be incorrect or lost. You can argue that SPDIF is just as unreliable but data loss would only be one or two bits (not several bytes) and with a much slower clock frequency, jitter is a significantly larger concern.
With that said, my BDP is stuck at using 2 1TB bus-powered drives until Bryston releases it's HDD enclosure (and it better not have wall-wart power supply!

).