This is a fairly interesting amp. This amp seems to be able to behave as a voltage source or current source depending on headphone out. I used my HD600s to check out both ports.
Out of the voltage out it sounds pretty pleasant. More lower end impact and fun factor. Still, I wouldn't call this as overtly colored sound at all. In fact I like what I heard quite a bit. Good amounts of power reserves (though they seem to get consumed rather fast... this is sort of a rechargeable amp which adds to it's uniqueness)
Anyhow, using the current out definitively adds quite a bit of hump. It's a completely different story now. Hell of a lot more gain too. This is not subtle.
Here are some frequency response plots of my HD600s out of the 2i2, Bakoon voltage out and Bakoon current out:

Out of the voltage out I measured somewhere between 1.5 to 1.76 ohms output impedance. In current out all bets are off. There is a low and high gain switch which seems to do a whole lot of nothing when using the voltage outy. However, it does control gain of the current outy.
So from the voltage output I was able to get 3.39 Vrms into an open, 3.37 Vrm into a 300 ohm load, and 3.24 Vrms into 33 ohms.
From the current output in high gain mode I was able to get 9.78 Vrms into a 300 ohm load, and 3.3 Vrms into 33 ohms. In low gian mode I was able to get 5.57 Vrms into a 300 ohm load, and 0.626 Vrms into 33 ohms. Into an open I got all kinds of weirdness.
As far as THD, different results depending on the output port. All of the following were taken @ around 400mVrms and -6dBFS from the Focusrite DAC line out. Current output was in high gain:
THD 1 kHz 300 ohm (voltage out)

THD 1 kHz 33 ohm (voltage out)

THD 1 kHz 300 ohm (current out)

THD 1 kHz 33 ohm (current out)
