To prevent an XY problem, here's the context:
A striking feature of the 777 is how small and thin its tail fin is compared to the 747.
When I asked about this many, many years ago, someone told me it's because of the 777's fly-by-wire, which makes better use of small fins. But I started to question that recently.
Above are overlaid scaled drawings (747 and 777). Right away the engine placement seemed to provide the answer: one engine inoperative (OEI) controllability.
Using each plane's lateral engine placement and max thrust (282 kN and 513 kN for the 747-400 and 777, respectively), and with a worst case scenario OEI for the 747 (which would be an outboard engine), the 747 ends up with ~27% more yawing torque. Which would explain the tail fin areas of ~77 and 53 $m^2$.
But (big but), I recalled a famous A340-600 OEI takeoff video (a quad just like the 747 and with equal thrust of ~280 kN), and decided to compare it with the 777-300.
And here the tail fin areas are ~53 (777) and 48 (A346) $m^2$:
So, back to square one.
Of course there's the upper-deck (hump) of the 747; if that is one of the main reasons for the bigger tail, then it still does not explain how the A340 (-500 and -600) manages its OEI by having a smaller tail and more outboard engines compared to the 777.
Is it really fly-by-wire that permitted the smaller fins (area and thickness) of the A345/6 and 777?
One possibility that came to mind is perhaps the use of asymmetric spoilers when an extreme yaw is commanded – which can be seen in the linked A340 video at one moment (before/after the ailerons showed big deflection without the use of spoilers). Of course that presents its own problem: the accompanying roll (and with the video's low-quality and lack of telemetry, it is not really evidence).
Tail fin areas via https://booksite.elsevier.com/9780340741528/appendices/default.htm
Scaled drawings via Boeing and Airbus (for the 777 I used the -300, not the -300ER, in case you're wondering about the wingspan).