Persian Empire was older and larger (I am not sure about this) than the Roman Empire. However, when it comes to the title of Superpower, many historians say Rome was the world first true superpower. Why is that?
As the commenters have stated, there are several reasons
- "Persia" isn't one empire, but a succession of empires controlling the same area, more or less in the period. Rome under the Republic and Empire was a single continuous government.
- The various Persian governments tended to get knocked around in head to head competition with Mediterranean powers. The Greeks beat Cyrus and Xerxes, Alex conquered the entire empire, the Seleucids lost to Republican Rome regularly, as did the Parthians and Sassanids aside from a few notable wins.
- Bias, since we just know a lot less about the Persians than the Greek and Roman states.
Rome, on the other hand, did dominate the entire civilized Mediterranean basin for a long time - which nobody has managed to do before or since.
I conjecture that there is one more reason. The historians you mention belong to the "Western European/North American" culture. It is a direct descendant of the Roman empire (in the cultural sense).
Perhaps if you read Persian historians you obtain a different picture.
And I am sure that if you read Chinese historians, you will learn a very different opinion on what the first true superpower was.
EDIT. From reading Herodotus and Xenophon one can indeed conclude that Persian empire was a "superpower". Unfortunately its literature did not survive. And our perception of the ancient history is mainly based on the rich literary heritage of the Greeks and of the Roman empire.
A lot has to do with the successor states that were spawned by the respective countries.
Rome spawned a number of successor states in western Europe (albeit a millennium later) that created the printing press, and one of the offshoots of these western European states was America, which created the Internet.
The Sumerians may have been among the first to create writing in clay and parchment, but later versions of the Persian empire (e.g. Iran) were not nearly as successful at creating means of communications to tell their story as Europe and America.
It's possible that Persian (or Indian or Chinese) historians have a story to tell that is lost in antiquity, because these countries obtained the printing press much later than the Europeans, and failed to create the equivalent of e.g. "The Cambridge History of Europe."
But it remains a truism that "history is written by the victors."