I recall also being somewhat confused by the different versions when previously considering some bar changes. The Fairweather is definitely wider at 710mm and has less backsweep, less extension, and no rise it seems:
I have a tig'd B904 threadless I acquired via trade and can at least confirm the one in my possession has the same Riv shape, extension, and rise, but with a narrower 610mm width compared to the 660mm B901.
It looks like the two fillet brazed versions (quill and threadless) Riv last stocked were both labeled as B901R on their site so maybe the R represents the fillet brazed vs. TIG construction?
Not entirely sure but my own prior conclusion was the following:
B901 = 660mm Riv shape
B903 = Fairweather 710mm threadless
B904 - 610mm Riv shape
Hopefully some others could confirm/deny any of the above or have one available (as both my quill 901 and threadless 904 are in use and not what you seem to be looking for anyway.)