Note: This first paragraph does not directly address your question, but gives important information for the second part that addresses it.

Basically, the Roman army changed in a couple ways throughout those years such as through tactics, weapons and styles of fighting. First of all, with those thousand years come experience. From the Persians to the Goths, the Byzantines acquired knowledge of how to combat almost any kind of opponent they faced, as written down in Tactica by Emperor Leo VI (895–908). We know that by the time of Basil II, weapons of longer reach than the Gladius (short sword) were standard in the army to counter the longer reaches of some Barbarian weapons, the Kontarion Spear and Spathion Longsword were both adopted to make up for the short reach of the Gladius. Also, from fighting against the Sassanid Persians, the Byzantines had learned that rather than having their foot soldiers be destroyed by horse archer arrows at a distance or be smashed by heavily armored, mounted horsemen called Cataphracts, they would adopt these ideas and integrate them into their army, making it a less infantry focused fighting force.

Now, this sounds unrelated to the question, but alllow me to get to my point, because what I have said is important to the context of what Ill add next. Basically, all these changes and advancements indicated how much versatile this fighting force was and how it adapted. In order to allow for such widespread adaptations of new tactics in a standard army of the time, there must be adequate communication, chains of command and succession of that change of command as well as a centralized authority (the Emperor). All this the Byzantine army had. I would argue it was more organized than the old Roman Legions because of that final point: Loyalty to the Emperor and his successors. In the old empire many emperors, such as Galba, Vespasion and Septimun Severus, among others, came to power because of the support of either their legions winning a civil war or being appointed by the Praetorian Guard (the secret service of the Roman Empire) after the previous Emperor was deposed... by the Praetorian Guard. In short, from 114 AD to 1114 AD, the Roman Empire may have shrunk in size, but with that it became much more centralized and bureaucratic.

Edit: After being, understandably, called out for the part about me actually answering your question being a bit short, I'll add some more. Another way the military changed was in religion. The much more centralized Orthodox Christianity meant there was much more religious unity in the ranks rather than the many warrior cults and syncretic religions that persisted in prior the the Christianization of the empire. Also, now their commander in chief was not only their head of state, but also the head of their religion. This is from Caesaropapism (Caesar over Pope) where the Emperor was the highest power in the empire, unlike in say the catholic Holy Roman Empire, where technically the Pope was the highest power. This affected the army by making many of its allies reasons for fighting alongside them their religion rather than their power or wealth. This is most famously seen in the First Crusade, when Western Catholics conquered Jerusalem (supposedly) in the defense of Eastern Christendom when it was beset by the Seljuk Turks.

Sources:

Byzantine and Modern Greek Studies, 31 (2007)

Dennis, George T. (1985), Three Byzantine Military Treatises, Washington DC

Dennis, George T. (1997), "The Byzantines in Battle", in Tsiknakis, K