Rather than pinning all of the differences only on the USB cable vs the SPDIF one, which are passive components, keep in mind that we also have two substantially different active circuits involved, as antigrunge2 has already noted.
I'd give it good odds that the more natural sound you're hearing from coax may in your case be due to nothing more than it is a better circuit and more suited to quality audio than your USB option. (And, keep in mind, there is sending circuitry at the Aries end and receiving circuitry at the RME end, so even there the "blame" could be only in the USB circuitry at one end of the chain, or alternatively, the interaction of both ends.)
However, to me it doesn't seem to be a hard decision to go with the better sounding one.
I'd give it good odds that the more natural sound you're hearing from coax may in your case be due to nothing more than it is a better circuit and more suited to quality audio than your USB option. (And, keep in mind, there is sending circuitry at the Aries end and receiving circuitry at the RME end, so even there the "blame" could be only in the USB circuitry at one end of the chain, or alternatively, the interaction of both ends.)
However, to me it doesn't seem to be a hard decision to go with the better sounding one.