It makes no sense whatsoever. The AX1 is a 1/2.3" chip, and since it only uses a crop of that (8.3 million out of about 19 million total photosites) the used area is a little smaller even than 1/3".Would it not make more sense to compare the Sony AX1 4K with the DVX200 4K?
It has already been done, and the DVX200 looks like a winner: https://vimeo.com/146203898
As a first approximation, the DVX200 chip is approximately 16 times the area of that used in the AX1 - which should give it a 4 stop advantage over the AX1 if all else was equal. (Probably more, as the interpixel banding won't scale up proportionately.) All else isn't equal, as against that the AX1 has a faster lens in terms of f stop, by about 1 1/2 stops. So theoretically the DVX200 should be predicted to have an overall edge of about 3 stops.
And that video shows something pretty close to that, maybe more like 2 1/2 stops. Hardly surprising. (And why colour balance to 5600K for a tungsten lit test? Why use such a fast shutter speed?)
Since there aren't any other 4/3 video cameras around, if a comparison is to be done, surely far more sensible to do it against a 1" sensor or s35? Comparing a cropped 1/2.3" sensor with 4/3 is pretty pointless.

