2-Piper:
"Personally I think the Purdey double bolt is a superior design."
Care to elaborate? The three guns I have come across with round underbolts are the Mod21, Horsley and a Belgian Darry. The underbolts were in the 9mm diameter range, offering 60 square mm against shear forces. The Purdey underbolt offers slightly less cross sectional area in most English style guns.
Additionally the round bolt seems easier to drill, fit and finish at the manufacturing and repair phases.
To the round underbolts you can add the Ithaca Flues & at least some Crescent Arms guns, my American Gun Co hammergun has one.
All single bolts of which I am familar, whether round or flat, bolt into the bbl notch at the extreme end. There must of necessity be clearence enough for the bolt to run freely, thus the actual load bearing area of the bolt to the frame is a minute point of contact. With the double bolt on the other hand the lug penertrates the bolt. The bolt thus engages the frame evenly on all four sides of the lug, It don't need near as much metal to carry an equal (or greater) load. In addition on the Purdey bolt, as well as most of its copies, the forward face of the rear lug is cut on a radius swung from the center of the hinge. Frame cross section is mated to this radius with just minimum clearence to open & close. There is thus a load bearing area here to resist the axial thrust of firing much greater than that of the hinge pin. The entire back thrust of the 21 is carried by the hinge pin alone.
Again winchester just depended upon good Metallurgy to make up for what others of necesity, when basically all they had to work with was mild steel, took care of by design.