Army sizes tend to depend more directly on the way in which a community's armed forces are organised. The city-states of Classical Greece fielded relatively massive armies, because they habitually levied the entire male population aged 18-60 for brief local campaigns. Larger empires generally could not do this, firstly because it would paralyse all economic and agricultural life to send the entire population marching across vast distances at the Emperor's command, and secondly because it would be impossible to manage, feed and tactically deploy such a vast army without significant advances in communication technology that were not made until the 19th century.

For this reason, despite all the Greeks' outrageous claims about the size of Persian armies, their own combined levies probably matched or even outnumbered the Persian expeditionary force at the decisive battle of Plataia in 479 BC. If Herodotos is right to tally up the Greek forces at nearly 110,000, that would have been one of the largest armies the world had ever seen. Despite having a population of many millions, the later Seleukid Empire (which largely overlaps with the Persian Empire but for which our sources are better) never fielded an army larger than 160,000 men, which has been regarded as a theoretical maximum for the logistics of the time.

As states developed increasingly sophisticated mechanisms for levying troops, this tended to result first in a dramatic increase in army size, and then in a reduction as the focus came to lie with professionalism and effectiveness. Once Rome grew to a respectable size, it never again levied its entire population, choosing instead to raise as many legions as it needed to win a given war.

I'm not an expert on later periods, but as I understand it, the armies of the 16th- to 18th-century Europe also tended to be relatively small, well-trained, and mostly composed of mercenaries; it wasn't until the French Revolution that the potential of a vastly increased population size was tapped for military purposes.