My experience with different calibres on dangerous game.
I have used 9.3X62, 375 H&H, 458 Lott, 450 Rigby and 470 Nitro Express.
Although I absolutely love the 9.3X62 and it may just be my all time favourite cartridge it does feel a bit light in your hands when you are in a situation with a DG animal that is being reluctant to go down. The 375 H&H felt the same for me, did the job fine but just didn't have that feel of authority and hitting power when firing follow up shots.
We all know shot placement on the first shot is all important but that's not what this discussion is about.
From my experience and IMHO a cartridge producing enough energy to more likely potentially turn an animal like a buffalo without a brain or spine shot starts at around the 5000ft/lbs of energy. Will a 9.3, 375, 450/400 also do the job, in many scenarios those cartridges probably would, in some scenarios probably not. Will the bigger cartridges always turn an animal without a brain or spine shot, probably not but obviously the bigger cartridges are more likely to achieve this than the smaller cartridges.
I also consider going away shots just as important for a "stopping rifle", maybe not as important as in life or death for the hunter but just as important as in recovering the animal. There are far more scenarios for both a client and PH having to take shots at an animal going away that isn't mortally wounded than taking shots at an animal charging that isn't mortally wounded. Again, can the 9.3's 375's, 450/400's etc hit the animal hard enough and do enough damage to either slow it down or completely stop it when running away, yes 100% all those cartridges can potentially do that and do it quite well but will the bigger cartridges do it better, yes 100% they will.
I feel that if you are having this discussion in your own head and having a "stopping rifle" makes you feel more comfortable then use a rule of thumb that makes sense, 4800-5000ft/lbs as an example is probably a good starting point and then choose your rifle and cartridge based on this.