Feel free to discuss and consider this proposition in the comments.
I will briefly comment that during a visit to Greece, and in particular, some tours in Athens last summer, the Greco-Persian War was vibrantly alive in the hearts and minds of the Greek people and still felt relevant today.
Of all the many counterfactuals, those “what-ifs” posed by history, perhaps the most arresting, if only because the most sweeping, asks: "what if the Persians had defeated the Greeks in the Greco-Persian War of 490–479 B.C.?"
Had this happened, there might have been no Plato, no Aristotle, no Roman Empire, no Christianity, no Western Civilization. A Great King, a lineal descendant of Darius, might still rule the world. All might worship the Zoroastrian god Ahura Mazda, with men going about in turbans, women remaining at home or in harems. But that, as every counterfactual invariably ends—generally accompanied by a sigh of relief—didn’t happen.
From this book review reviewing Peter Green, Xerxes at Salamis (1970, reissued as The Greco-Persian Wars).
I'll also note that the answer is multi-faceted.
One aspect of the question is a question of what matters in terms of historical causation.
If you are believer in the "Great Men" and "key moments" theory of history, events like this really can make an immense difference.
But, if you think that history is largely a function of big, long term fundamental forces like climate and technology and inevitable secular trends (an approach often associated with Marxist historical interpretation but by not means so ideologically bound), you may be inclined to say that if the Persians had defeated the Greeks in the Greco-Persian War of 490–479 B.C., the fortunes of the parties probably would have been reversed in a second Greco-Persian War of 453-444 B.C., without leaving the world notable changed in the long run.
In this view, "Great Men" may change the finer grained details of history, but only rarely the overarching long term trends that matter in the long run. The alternative history would surely be different in some respects, because history does not repeat itself, but it would rhyme with the world we live in, taming our utopian and dystopian instincts.
In the language of mathematics, historical causation is a "chaotic" process, i.e. one in which small changes in the conditions in one moment are capable of producing big differences in outcome down the line due to the non-linear processes involved in how events unfold. But, historical trajectories have an "attractor" to which the non-linear processes' developments tend to gravitate, although the strength of these attractors is not a matter upon which there is a strong consensus, even when it is possible to meaningful define or describe that strength with more than a mere gut feeling.
Even then, however, a question like this opens up the question of what is really fundamental, and what is window dressing.
An absence of Plato and Aristotle does not imply that the Persian tradition might have offered us equally formidable philosophers and proto-scientists. Cf. Hindu philosophy was mathematical. Indeed, some non-Western figures readily present themselves as alternatives.
We might not have "Western Civilization" but that is not to say that Persian civilization under the different conditions it would have encountered in the scenario suggested would have been all that different in the ways that matter. Surely, an ascendant global Persian civilization would have still been more similar to our "Western Civilization" than the civilizations of India, China, Japan, the expansionist Bantu tribes of Africa, or the Aztecs.
A Persian Empire, had it extended to Hadrian's Wall, would probably have turned out more similar to the Roman Empire than the Persian Empire of our history books, but it would surely also have been quite distinct in myriad particulars. The notion that "A Great King, a lineal descendant of Darius, might still rule the world", likewise, seems about as plausible as the notion that because the Greeks won, a Roman Emperor still rules the world.
The Roman Empire with late Iron Age technology, was not sufficient robust to survive to the modern day, and neither would a Persian Empire.
Arguably, the therapeutic deism of the typical layman with little training in religious doctrine, who is nominally Christian, is actually closer, doctrinally, to Zoroastrianism than to Christianity or Judaism understood at the level of the doctrines that matter to educated elites.
It could be that 19th century businessmen might have ended up wearing turbans rather than bowler hats or beaver caps and silk neckties, if this had come to pass. But, anyone who thinks that fashion has much intrinsic value vastly overestimates the importance of function over form.
And, the suggestion that in world where the Persians rather than the Greeks prevailed that we would have women remaining at home or in harems, misapprehends the extent to which women's roles are functions of economics more than culture.
King Solomon is a household name to every small town Christian and Jew in America, and he generally has a very high favorability rating. But, that doesn't mean that modern Americans maintain vast harems in order to follow his allegedly wise example. And, women remained at home to a much greater extent than they do today as recently as the 1950s and early 1960s Baby Boom in the United States.
IMPORTANT UPDATE (July 6, 2020):
One noteworthy aspect of Zoroastrianism is that, in contrast to other ancient religions (including Judaism, and later, Christianity), Zoroastrianism appears to have banned slavery on spiritual grounds. This is important to bear in mind in the context of discussing the Persian War, below. The Greeks thought of the war as the defense of their glorious traditions, including the political participation of citizens in the state, but it was the Greeks who controlled a society that was heavily dependent on slavery, whereas slavery was at least less prevalent in Persia than in Greece (despite the religious ban, slavery was clearly still present in the Persian Empire to some degree).