The Mede controversy doesn't really imply the lack of an "Empire" though. Whatever that really means. What it suggests is that the Medes were not a civilized peoples and did not build very many constructions, such as at Ecbatana, despite the assertions of Herodotos and others. So I would assume that Ecbatana was actually built much later during the Achaemenid period and then expanded upon greatly under later dynasties. Honestly some of these claims made by Herodotos about how Babylon looks or about the city of Ecbatana are completely wrong and it sounds like he just made it up.
The implication here is that the Medes were clearly tribal nomads who herded horses and probably sheep. Incidentally that area around Tabriz and Teheran are extremely well suited to herding. The Kara Koyunlu and the Safavids originated there as the dominant horse people of the area during their respective centuries. That the Medes had basically subjugated most of the region through a system of tribal alliances is not surprising given their history for warfare, as is related to us by the Greeks.
Their expansion into the Armenia, Cappadocia, and Arbela regions are actually not that surprising given this full context. Those are good areas for keeping horses and no doubt the Medes were also looking for plunder. Though as Herodotos states the Medes were also trying to remove the Assyrian yoke. As sumskilz just implied the Medes unleashed their mighty horde into the Assyrian heartland. This shows that they were indeed quite powerful. Such tribes do not sit idle for very long, I have no doubt that they subjugated many of the Iranian tribes. For example both Herodotos and Ktesias frame the overthrow of the Medes by Cyrus (Kyros, Kurosh, or what have you) as a war of liberation. Probably true but take these Greek sources with a grain of salt.
Although the Persians were similar to the Medes and were both Indo-Aryan peoples. The Persians seem to have been influenced by the Elamites. They could read and write cuneiform, they began to build settlements, and more importantly to distinguish them, they fought on foot with spears. Maybe because the mountainous terrain in south west central Iran is not conducive to cavalry. Chariots were reserved for the nobility. That is unlike the popular perception of the Persians as being horse riders, which actually comes from the Arsacid and Sassanid periods.
In terms of how powerful the Medes must have been... In order to dominate Iran and to actually carry on the fight against the Assyrians in their own territory it was necessarily considerable. For this period that is somewhere in the range of 20,000 if not 30,000 soldiers at its peak. But due to logistical constraints surpassing 30,000 men was not easy. There are ways around these limitations but they are finite, especially for an underdeveloped region. My assumption is that a good portion of this army must have consisted of cavalry. Likely 1/6th to 1/4th which for nomads to supply a massive amount of horses in the ballpark of 5,000 cavalrymen, and supplying this army was not impossible. At least not a society as large and apparently as powerful as the Medes. While the rest would have been spearmen and foot archers because they are mentioned as being part of the Persian contingents as well. Perhaps they had more cavalry than that but it is not really consistent with this time period and that is somewhat difficult even for nomadic pastoralists. Also consider that the Persians themselves made up most of the Achaemenid infantry.
I assume that this sedentary or semi-nomadic lifestyle eventually gave the Persians an advantage against the Medes. The Persians were apparently very capable at adapting. What I found interesting is that accounts of the "Persian Revolt" seem to imply some kind of mobile guerilla warfare with fall back positions in the mountains. Where the Median cavalry would not be effective and such a prolonged struggle might put the subsequent mutiny against Astyages in its proper context. Though if these Greek sources are correct then Cyrus was some kind of propaganda mastermind. Whether Cyrus actually adopted larger cavalry contingents and used them with his infantry in a combined arms approach at this time, similar to what we can surmise of actual Achaemenid armies, would be interesting to consider.
The Sassanid era tends to provide much higher density of wares and settlements than the Achaemenid period. In terms of material culture the Sassanid era comes off as an Iranian golden age. Where as during the Achaemenid period much of Iran appears desolate by comparison. Although a lot of foreign wares tend to show up in key areas like Susa. But most of the Achaemenid material within Iran tends to be found in places like Susa and Persepolis regardless. Weapons like Achaemenid arrow heads are found in large numbers in places like Egypt and Anatolia. Confirming that the Achaemenids loved to spam archers. But also that they were always engaged in warfare in those areas, or at least those areas had high troop presence... for whatever reasons. Probably having nothing to do with warfare. Right anthropologists, sociologists, and Achaemenid apologists?
A lot of the finds from this period are concentrated in the south west of Iran and actually around the Tigris and Euphrates. Not only did the Achaemenids conquer Mesopotamia/Babylon but it was their key holdings and they outright colonized areas of it. Since the Persians and Medes were the source of manpower for the Achaemenid armies, later the Bactrians and Sogdians as well, they must have resettled a lot of these in conquered lands in order to secure these territories. They undoubtedly wanted to expand their manpower base so giving lands to soldiers is a no brainer. The importance of Mesopotamia/Babylon and the lack of importance which much of Iran seemed to hold I think indicates that there wasn't really a national concept of Iran. The concept was new under the Achaemenids but actually appears to have developed during the Sassanian era.