Personally speaking, I just like things to be "pukka".

For me this means Euro chamberings for Euro rifles, and Brit chamberings for Brit rifles. American cartridges in American rifles too, for that matter.

Nicest 9.3x74 U/O double I have fired was a Beretta Gold Sable, and were I inclined towards stack-barrel rifles I could certainly be happy with that set-up. My eldest daughter was absolutely smitten with the Gold Sable!

In a Brit double, it would need to be a rimmed Brit cartridge, regardless of barrel configuration. Closest to the 9.3 would be the .360 No.2 as mentioned by John, and I do like the cartridge ever since playing with a hammerless SxS so-chambered many years ago. Mike's suggestion of the .375 Flanged Magnum is also excellent imho, and probably the logical favorite since the .333 would likely be more trouble than its worth these days.