In Medieval times there were more local conflicts than large scale invasions - it was a time of fragmented states (that's what the feudal system is about).
Plus, in Medieval times, people were paid to wage war, therefore keeping a large army was extremely expensive, and often you did not keep an army on your own but hired mercenaries to wage war with/for you. In Antiquity, I believe the reward system was different.
It pays here to look at a map of how small an average principality would be in medieval times versus how large Alexander's empire was.
The population densities were, it should be noted, not that different in the two periods. It was not until the mid-1700s that we started to see sustained significant improvements in the carrying capacity of the land thanks to agricultural improvements in England. Until then the carrying capacity would vary, higher during a warm period in the 1200s, falling significantly when things cooled down again in the 1300s.
Plus, in Medieval times, people were paid to wage war, therefore keeping a large army was extremely expensive, and often you did not keep an army on your own but hired mercenaries to wage war with/for you. In Antiquity, I believe the reward system was different.