The fact that there seems to be a hard cap on size of an overland army in pre-railway times is important. After all, various empires of the ancient world had hugely different population sizes; and in modern times, say, 1900, all other being equal, an empire with more people could have sent a much larger army to conquer its neighbors. That is what we expect.
But from Devereaux's studies on logistics, it seems that the premodern empires, after reaching a certain size, were "almost equal" when it came to military capability, and a lot of the (dis)advantages were on the quality side, such as good maneuvering and an ability to join two armies at precisely the same time.
It surely explains why the Romans never managed to crush the Persians, even though the Roman empire had a lot more resources to draw from. The logistics of running a really massive campaign against the East were too daunting.