We're not aware that they sound any different. One would need to do a proper scientific single or double blind test to rule out bias (I know, I know, but let's be honest, we're all inherently biased once we set our minds to something).
The real test would be the on DSP bypassed sound. You mentioned Vintage and Digital Delay presets sounding different with different power supplies. Are you sure you turned off all modulation? Many of those algorithms' presets have subtle, slow and non-deterministic modulation that affects the high end response over the long course (think 30 secs to a minute). Basically what I'm saying is rule out all the uncontrollable complexities to get a to trustworthy baseline. We did a fair amount of this while developing the H9 and migrating the algorithms.
The analog circuitry is a bit different due to H9 having input level adjustment, and we did do our best to match the gain staging. It's a possibility that there is a small, but measurable difference, but we did not find it to be actually perceivable, or at least negatively so.