FWIW - Gyphon is now available in the USA -- Suncoast Audio is the only dealer/distributor as of now (late July 2017).
I haven't heard the Berkeley Ref2, but have a Rossini and a Debussy. I sat and listened to the Vivaldi partial stack (no transport because everything was digital via Roon). The Vivaldi 1.0 still bests the Rossini, but it is a narrow margin.
The Rossini has approx 6 filters (depends on if you're listening to PCM or DSD). Once you get those figured out, it starts to show its stripes and you can no longer call it a "chameleon" -- but that is a good analogy for the Rossini. It's also way more geared up with tech than the Ref2. It has direct Ethernet and can directly stream Tidal and others (perhaps they'll make it a Roon RAAT supported device -- that would be awesome.) It also has direct USB inputs. I have to agree that the Ref2 is way behind still using that old school separate USB to AES converter.
Be prepared to shell out 1/3 the cost of the Rossini on the separate clock. It almost makes you consider a plain Vivaldi DAC since you're about 2K difference at that point. But the Rossini by itself sounds better than the Vivaldi by itself. It's when you put the two together with their clocks, and add the upsampler to the Vivaldi that the Vivaldi takes the lead.
Truth be told, the Debussy isn't a slouch when compared to the Rossini though. There are some characteristics that are better with the Debussy. I'd characterize the Rossini as "laid back", and the Debussy as "forward" in presentation.
I really would be interested in hearing someone's direct comparison of the Rossini vs the Berkeley Ref 2 just like the OP. Despite the technology differences, I am always more interested in the sound. It's hard to find a dealer that has both -- they're just in the top of the game so most pick one.