The details (as I see it).

H&H

Front sight(-protector)

Shape of the quarter rib

Stippling (parts of) receiver

Cheek piece

Rigby:

Surface treatment of the rib

Way (and for sure the content) of the inscription on barrel and receiver ring.

Barrel contour (shank and rear portion) is in between.

The barrel contour of this item (.404 Cal. ! )is something in between. It is found on Rigby´s up to .350 Cal.

and H&H usually made them up to .300 Cal.