Yes, or rather they fought armies similar to what ever Greece was actually fielding at the time. As u/Iphikrates discusses in this post, the hoplite and phalanx were both concepts in their infancy around the time of the Persian Invasions.

The Greek cities of Ionia were typically more or less on the same page as whatever trends their co-Hellenes in Europe were into at the time, maybe a little ahead of or behind them depending on the trend in question. For hoplite warfare, or rather "heavy infantry with big shields and six-foot spears in rows mostly separate from other units" warfare, they might even have adopted it first. The Greeks were hardly the only people to employ the same basic tactic. The Egyptians, Phoenicians, Mesopotamians (Babylonians being called Assyrians by Herodotus), Lydians, Carians, and Cypriots are all routinely described as employing either their own hoplites or bearing equipment that sounds an awful lot like the equipment used by Greek heavy infantry. On top of that, most of the peoples of Anatolia, the Caucasus, and Western Iran occasionally fought in similar formations with lighter armor and smaller shields.

The Persians had fought all of them, including the Ionian Greeks, well before even the Ionian Revolt. All but the Egyptians and Cyprus were defeated by Cyrus the Great between 550-539 BCE (or rather his generals in Ionia and Phoenicia). Cyprus and Egypt were conquered by Cyrus' son, Cambyses, in 525. Darius the Great then had to reconquer Babylonia (twice) and parts of Egypt just a few years later. Unfortunately, we're basically reliant on Herodotus as the exclusive detailed source for everything up to the 470s, and aside from a few key engagements in Greece, he doesn't provide much detail.

We do know there were a few pitched battles that must have featured hoplite-esque infantry over the course of all these wars: at Pteria c.547 against the Lydians (and their Carian subjects) , at Opis against Babylon in 539, on the Tigris River against Babylon in 522, at Ephesus against the Greeks in 498, at Cypriot Salamis c.497, on the Marsyas River against the Carians c.496, at Pedasos against the Carians c.496, and at Malene against Greeks c.493.

Many more pitched battles are probably implied, but not explicitly referenced, and if you count battles against enemies wielding lighter shield and spear tactics the number almost doubles from rebellions against Darius the Great alone. Most of those come from Herodotus' account of the Ionian Revolt, and out of all the battles listed above, only Pedasos was a Persian defeat and that one was a surprise attack at night. The Battle of Ephesus in 498 BCE is probably of particular interest to your question because not only did the Persians defeat the Ionian Greeks, but their Athenian and Euboean from European Greece allies just a few years before Marathon.

The both the Battle of Malene is described very briefly, but featured Persian cavalry pinning the Greeks in place with missile fire, forcing them into retreat in which they could be easily picked off from behind and along the sides. Essentially, if the Persian ranged units could get at the sides that were not easily defended by their large shields, the advantage of hoplite equipment was nullified. The speed needed to catch up with the Greeks before they could board ships at Ephesus at least implies a similar tactic because it would have necessitated a cavalry attack. The other highly effective tactic when outarmed by the opposing force was to spread around some well placed bribes and get a portion of the enemy force to retreat, either inducing a full retreat or creating a weak point in the line. That was showcased in the Battle of Cypriot Salamis.

I'm guessing this question is at least partly inspired by the popular, but inaccurate, belief that the unique power of the hoplite-style was the key to the Greek victory over Persia at Marathon, Plataea, and the Eurymedon river and the strategic defense at Thermopylae. If not, or maybe in addition to, that idea probably the equally popular but inaccurate belief that the Persians turned to Greek mercenaries after 479 BCE to make up for their own inadequacies. Neither is true.

To address the latter issue first: Greek writers liked to focus on Greek stories. So when mercenaries showed up, they got a lot of ink on the page, but even the largest Greek mercenary forces recruited by the Persians were dwarfed by the regular subjects in the army. Repeated wars in Greece during the 5th Century BCE just created a large market for mercenary soldiers in between conflicts at home. The Persians had near-limitless money and the Greeks were already at hand when soldiers were needed in the west, why wouldn't they hire mercenaries?

More importantly, all of the similarly equipped peoples we've been discussing, from Ionian Greeks to Egyptians and Babylonians were Persian subjects. Barring a few particularly chaotic moments in the reign of Artaxerxes II, the Persians could simply recruit heavy infantry all on their own.

The question of the hoplites as some sort of indominable battlefield force is another matter. For a more detailed description about the Greek end of things, I'll direct you to u/Iphikrates again: here for Greek light troops and here for the misunderstanding of hoplite dominance. I'll probably overlap a bit with those answers below.

The idea that the Greeks just dumped mass quantities of hoplites onto the field all alone is erroneous and outdated. Every Greek city had huge quantities of people too poor to fill that role and equipped them as archers and skirmishers on the battlefield. Athenian archers in particular are credited with saving their hoplite countryman from Persian cavalry "pin-down and retreat" tactics in the prelude to the Battle of Plataea. They also had their own cavalry forces, but since the phalanx was notoriously vulnerable to cavalry charges that could simply outpace the men on foot, cavalry was usually just to keep enemy cavalry away from the infantry.

More importantly, all of the supposed great victories over the Persians by hoplite forces are brimming with caveats. At Marathon, the Persian cavalry was mysteriously absent. The best theory is that after getting stuck on beach for several days with the Athenian army blocking their way uphill, the Persians started getting ready to leave and land somewhere closer to the city itself, prompting the Greek attack once the horses were already back on the boats. The whole situation gave the Greeks every advantage in the world, charging down hill at a an army with their backs up against the sea and a river with swamps to one side. Even then, when the Athenian center was strectched thin, the Persians broke through and got behind them, just not in time to prevent the Greeks from breaching the Persian camp.

I'll note Thermopylae as a famously successful Greek engagement even though it was a Persian victory. Once again, the Greeks had the benefit of terrain: holding a very narrow pass with cliffs to one side and sea to the other, a perfect place for a block of long spears and broad shields to form a wall and prevent the enemy from moving. In the end, that worked against them, the Persians got behind the Greek line and wiped them out from the undefended rear in terrain that made it equally difficult for the Greek formation to reposition itself.

At Plataea, you've got a more interesting situation in which the two forces may have been equally matched, rather than the typical Persian numerical advantage, and equally Greek. Though scholars typically dismiss Herodotus' wild claims about the 2 million man Persian army, they usually accept his significantly more realistic numbers on the Greek side. To estimate the size of the Persian force, we have to turn to the size of their camp and arrive at somewhere between 70,000-100,000 for Persia and the same for the Greeks, but there is a catch. Herodotus reports about 50,000 Greeks in the Persian army at Plataea, recruited from the cities and islands they already controlled from Boeotia all the way up through Greece and Thrace and into Anatolia. So this was a Greek on Greek battle with a Persian side-show, primarily in the cavalry.

Herodotus also attributes the Persian defeat to a pre-mature charge, in which the Persian general mistook a Greek repositioning for a retreat and tried to seize the opportunity only to meet Greek formations head on. It's also worth noting that Herodotus indicates that the Spartan and Tegean formation that first clashed with the Persian side was mixed heavy and light infantry, not pure hoplites and that the famed Spartan defeat of "naked" Persian infantry probably suggests that Spartan hoplites were slaughtering lightly armed skirmishers.

Finally, Eurymedon was actually two naval forces fighting on land when the Athenian navy reached the Persians before they could board their ships. This is perhaps the most one sided engagement on the list equipment-wise. Early Athenian marines were essentially seaborne hoplites, while Herodotus describes most of Persia's sailors with a variety of lighter equipment, most notably a heavy concentration on swords, axes, and missile weapons rather than pikes. Its one of the few engagements where the disparity in equipment probably made a huge difference, not because the hoplites were a better form of army, but because the Persian navy wasn't really intended for that kind of combat.

I cannot answer this myself, and I neither could I find an earlier answer on this question specifically, but from what our eminent u/Iphikrates has written before it seems Greek armies did not differ much from each other west and east of the Aegean.

In this thread he explains how the hoplite army was developed by the Greeks in the 6th century, and notes that "[Persians] faced it first during the hard-fought Ionian Revolt". And he discusses the victories and losses of Persians against Greeks before and during the Wars here and here, wherein he also points out that several other Eastern Mediterranean peoples had similar fighting styles to the Greeks, commenting that "it would be absurd to suppose that the Persians encountered some unheard-of approach to pitched battle when they invaded mainland Greece".

Edit: the hoplite army development of course happened in the sixth century, not the fifth, counting negative centuries can be difficult!