You have two areas of civilization, the Mediterranean and the Near East. After centuries of struggles among minor states, they are united under the Roman Republic and Achaemenid Persia. But these 'universal empires' were both huge deviations from the mean; they had no precedent whatsoever.
The Near East produced, at intervals, Akkadian, Babylonian, Hittite, Assyrian and Median empires. Each group typically controlled a geopolitical region which they had difficulty expanding beyond, such as Mesopotamia or the Taurus mountains. The Mediterranean was dominated by city-states, which squabbled over territory in typical thalassocratic fashion but didn't form lasting empires. Somehow, the Achaemenids wound up controlling half the world's population and Rome not only possessed the entire Mediterranean, but conquered their way up to Scotland. And these were enduring states of affairs. The Achaemenids ruled for two centuries, the Romans remained united for three.
I think there is rather more to it than lazy explanations like "the Romans had a professional army" or "the Persians respected indigenous cultures." In fact, I'd say that the characteristics of each empire aren't as important as their circumstances.