Yet another DAC I found that has both S/PDIF and USB: The S.M.S.L. Mini DAC Sanskrit. While the noise floor is generally lower in S/PDIF, it is peppered with jitter components that are much more problematic as far as audibility
That trace shows clear evidence of a 250Hz (ish) square wave getting into the clock.
The output signal has symmetric spurious sidetones, at 250Hz, and odd harmonics every 500Hz. The symmetry around the output signal suggests either strong coincidence, or spurious on the clock. The first sidetone tells you the fundamental of the clock spur (250Hz), and the odd harmonics tell you that it's due to a square wave injected into the clock generation.
You'd need to look at the system design to see where that 250Hz is coming from. Interestingly, I note that 48k/250 = 192. That's an 'interesting' simple binary value (128+64). My suspicion would be that there's a clock recovery/locking adjustment going on every 192 samples... Basically, it shows that the clock recovery/locking mechanism is pretty poor.
Some of the other traces here show the effect of the clock loop filter, as the noise floor dips slightly around the output signal, showing how the loop filter is actually reducing close-in (wideband) noise.
It would be interesting to see the effect of changing the SPDIF clock frequency, and seeing how the output spurii change; if you can match the source and destination clocks, you ought to disturb the destination clock less (not having to work as hard to lock to the source clock), and so the magnitude of the clock spurii should be reduced. Either a decent clock synthesizer & divider, or a simple pulled xtal ought to do the job.
A general comment to the thread: listen to Cosmik; that man knows what he's talking about.