I like where you're going with this but I don't think the Northern Empire -- the faction lead by traditionalist oligarchs who think that things should go back to the good old days of the republic -- would be too keen on adopting barbarian flourishes in their armor. They're in the northern part of the Empire but it's hardly frigid there. The Northern Empire is likeliest to be most traditionally Calradian (but this should probably look late Roman, not republican Roman -- something that looks like a dated but immediate predecessor of the current Byzantine flavor Calradic Empire and looks very ornate with stylized echoes of more classical stuff). Late Antiquity gets rarely used in games, whereas classical Roman and Byzantine both get used all the time. I think the Northern Empire, based on the lore, would fit a Late Antique Western Empire vibe pretty well.
Wee can see existing imerial regional variation in how the imperial crowns are set up, which are currently the only regional Empire equipment.
The Northern Empire battle crown is a late antique jeweled Roman ridge helmet -- from the late Empire, but covered in jewels and likely based on crowns worn by Roman emperors or high imperial officers. The Northern Empire civilian crown is a laurel wreath, which is the traditional Calradic crown-that-is-not-a-crown worn by Calradian emperors from Arenicos back to the beginning (see the Empire's original faction blog entry). Northern Empire troops are likely closest to traditional Imperial professional legions in style, though I think they should again have a Late Antique appearance so that they look like the immediate predecessor of the current Byzantine vibe that Arenicos brought in instead of something from centuries long ago.
The Western Empire battle crown is ALSO a late antique Roman ridge helmet, but it's more simplified and lacks the jewels. The Western Empire civilian crown on the other hand, is nearly identical to the Southern Empire's civilian crown with some minor differences in the jewels. In other words, the Western Empire takes elements of both imperial tradition (Northern) and dynastic innovation (southern) but uses them in a more military fashion. Since Garios's name is based on Arenicos that makes sense. I also expect that since Garios is next to the Vlandian frontier, this is a place where geographic adoption makes sense -- the Vlandian guard being the former bodyguards of the emperor (this is an innovation of Arenicos, but Garios would likely try to imitate his military glory and proclaim he's a better heir to Arenicos than Ira is). They probably adjusted their tactics and equipment to deal with the Vlandians.
Finally, the Southern Empire's battle crown is a crowned helmet based on a Byzantine model (technically based on St. Stephen's crown from Hungary, but that is a modified Byzantine imperial princess's crown) and their civilian crown is the bottom band of the same crown (which is the most Byzantine part of it). So while the entire Calradic Empire is "Byzantine," the Southern Empire is probably the core of the Empire of Arenicos and would use the most Byzantine-style troops that he brought into play.
tl;dr: we already see regional variation in the three empires based on the design of imperial battle and civilian crowns, and based on the lore, and Imperial equipment variation should follow the same pattern of Northern Empire == Calradian republican tradition with Late Western Imperial Roman appearance, Western Empire == military innovation and adaptation, Southern Empire == the most ornate and courtly Byzantine elements. There should be some military adaptation based on the foes each empire is facing, but primarily the differences in the three Empires should be based on the personality of THOSE parts of the 3-way civil war and not just on their barbarian opponents.
