During WW1 maybe 10 million people were killed. During WW2 50 million people were killed. Since the end of WW2 over 100 million people have died in various conflicts around the world.
Therefore a post-WW2 cartridge is likely to be the biggest killer and its probably the 7.62x39.
Not sure if the 100 million number is even close to correct, but it would be fairly important when the casualties occurred to make a stab at what cartridges were used. For example in Korea, many WWII firearms were used by both sides, also in the middle east and africa up to and including the '90s in many cases.
I would argue that the 8mm mauser round would be number one, 7.62x54 and 7.62x39 would be close.