Well. There's arguably grounds for them having at least some minor differences. Since even as a whole Empire. The different armies would have been situated in vastly different areas. So the Army stationed in the west would likely have had some differences more suited for fighting Battanians and Vlandians. While the Northern Imperial Army facing Sturgians and Khuzait more commonly would have had adaptations made to fight it better and so on with the Southern Empire.
Additionally the three different "Emperors" with different political bases could arguably also create further differences. I mean Garios with all of his Veteran troops as his base would likely be able to scrounge up some better Foot infantry in some way. Meanwhile Rhea as the Empress would likely have access to the Imperial Bodyguard, Praetorians, Scholae, Palatina or whatever you want to call it.
Toss in different recruiting bases and access to resources and there is easily room for the different Imperial factions having *some* variations in army compositions for example.
How to do it would be another matter though. Perhaps some have different branches or possibly they end in different things. The Western Empire could for example have better Legionaries. The Southern empire Stronger Cataphracts and the Northern Empire.. Better Buccelarii ?
Just some quick suggestions off the cuff anyways. It could also be minor variations in equipment. For example Western Empire has more Chainmail heavy troops, northern a bit more Northern looking Lamellar and Coats of plate with the Southern empire retaining the more traditional Byzantine look we know of.
