I don't know if it's appropriate to ask for a source for a question, but is there a source for the assertion that the post-split Western Roman military is glamorized, and when and in what circumstances was it glorified? Because from what I know of Roman history, the glamorization of its military comes from the pre-split military history, from the time it was growing as an Empire.

To answer this question we first need to establish some definitions. Namely, how do we define effectiveness? The first thought to come to mind might be, "who won the most", or "who conquered more" but this would be a discussion most of us already know the answer to. Instead I will be approaching this question from a slightly different direction: what were the Roman State's objectives and how did the military of the time help the Roman state achieve its goals?

During the middle and late Roman Republic, the Roman state's goals were primarily to build esteem, glory, auctoritas, dignitas, and, to a certain extent, material wealth for members of its governing body, i.e. the Senate. This is an oversimplification I will be the first to admit, however, the point still stands, Caesar, Pompey, and many others were highly motivate to win military glory by conquering foreign adversaries to distinguish themselves from their peers. In this sense, the Roman army of the Republican period was extremely effective. Probably one of the most effective military institutions of all time. Not in the sense that they won every battle (they didn't) or never suffered embarrassing and crushing defeats (they did), but in the sense that they always accomplished what they set out to do. Even if they lost, the Roman state had the political, social, and cultural determination to win eventually.

This outlook changed with the ascension of Augustus to Princeps. No longer was the Empire focused on territorial expansion or even winning glory, in fact this could be a bad thing. Too much success for any man that wasn't the Emperor was negative and could destabilized his position. The objective during empire was the maintenance of status quo, with a few exceptional conquests here and there. This was accomplished through stationing large army groups on the Roman border, who would periodically raid over the border to display Roman strength. Rather than reacting to enemy raids or offensive movements at a local level, the empire would proactively or punitively campaign in enemy lands. In the event a large hostile force moved into, or materialized within (e.g. a rebellion) Roman territory, Roman strategy dictated an immediate interception by the nearest army, and destruction of the enemy in a pitched battle. Examples of this type of power projection are Drusus, Varus, and Germanicus campaigning across the Rhine without serious attempts at holding territory. However, this strategy required large Roman forces, stationed on the borders, capable of smashing foreign targets with overwhelming force. This system largely broke down during the crisis of the third century where more and more border armies were pulled into the interior of the empire to fight in civil wars. Lack of Roman presence across the border encouraged settlement closer to Roman territory, and eventually lack of Roman presence on the Roman side of the border encouraged offensive movements by Rome's adversaries. When these offensive action were more seldomly retaliated against, this only encouraged more, and deeper movements into Roman territory.

Diocletian began to address a more local need for defense by pulling field armies, or comitatenses, back from the border to more able react to enemy movements and establishing the border guards, or limitanei, on the border to stop smaller attacks before they made it into Roman lands. Despite the reforms, the system was not effective at combating the large number of small groups coming over the borders of the Western Empire, primarily the Rhine. When the emperor Julian was made co-emperor and sent to Gaul in ~355 CE, the Gallic provinces were in disarray. Large Roman settlements on the Roman side of the Rhine (e.g. Cologne) are destroyed and Julian was besieged at his base in Sens, almost 300 miles inside of the supposed border, the Rhine. Julian was able to successfully establish some sense of order in Gaul through effective military leadership but once he headed east the fortunes of the Gallic provinces would only continue to decline.

During the late Roman period, Rome's primary reaction to military aggression was to attempt pitched battle or an offensive siege. Both options are risky, especially if overwhelming military force is not employed. Rome was still in a strong position, but could not reliably win the same stunning victories they had during the Republic and early empire. Even with capable generalship Roman forces could still lose when faced with roughly equivalent opponents, a good example being the second Roman defeat at Carrhae under Galerius. It wasn't until Galerius waited for significant reinforcements that he was able to defeat the Sassanids decisively at the battle of Satala. If the reinforcements had not been available, or if the battle of Satala had gone differently, two of the most valuable Roman provinces would have been undefended to a Sassanid advance. The battle of Adrianople is another example of a large late Roman force, not waiting for overwhelming advantage, losing to an invading force, in this case decisively. The late Roman state was simply not able to stop invaders at the border and unreliable in defeating them in pitched battle once they entered Roman territory.

Despite setbacks, Rome was still unstoppable if enough resources were concentrated. Galerius after Satala, Maximian, Stilicho and Aetius were able to concentrate large armies that were broadly successful in pitched battle. For example Stilicho's victories over Alaric and Radagaisus. However, even though Stilicho and Aetius were able to protect central authority, Rome's ability to project power through the provinces was declining in the West. The Roman military system was not able to react quickly enough to the changing demands of the political and military landscape. When the Vandals, Alans, and Suebi crossed with Rhine in ~406 CE, there was no serious opposition on the border or further inland. The Suebi were able to settle all the way in Spain and the Vandals in distant Africa.

Rome's military shortcoming during the late empire also lead to a decline in economic prosperity. In part because the Empire didn't have a coherent strategy to protect their economic assets. The late Antique Roman economic base was vulnerable, primarily farmland with no protection outside of the closest army. No scouting of cross border enemy action appears in the sources, no documented effort to give warning of imminent attack to civilian population, and a lack of options for civilians even if given time to react. Cities were vulnerable, despite Rome's attackers lacking effective siege craft, economic and administrative centers were still threatened and destroyed. Cologne, Florence, and even Rome to name a few. East Rome was focused on maintaining its administrative and economic base and not able to assist Western Provinces significantly during fifth century. The potential for large scale offensive operations in ended with the disastrous campaign in Africa under Leo I. Fortress Constantinople, geography, and a passive Sassanid Persia allowed the Eastern Empire to make it through the period mostly intact, despite the military apparatus being prone to the same shortcomings as their Western Counterparts.

Now that we've gone over the Antique Roman state's objectives and ability to accomplish those aims we need to take a step back and talk about terminology. As the Roman and Byzantine states are part of the same continuous polity, there's no clean break in distinction between one and the other. I can't point to a date and say all Roman military achievement before with date is Roman, and everything after is attributable to Medieval East Rome or Byzantium. Because of this difficulty I'm going to largely gloss over the transitory period between the classifications and focus on separating the periods into mostly Roman, i.e. prior to Theodosius splitting the administration of the Empire into East and West in 395 CE, and mostly Byzantine, i.e. the reign of Heraclius. I've seen the Byzantine period started as early as 284 CE with the ascension of Diocletian, or as late as the loss of the eastern provinces to the Arab invasions of the 630s CE, however, I'm not trying to argue where the bookmarks are, just to give some general ideas on the time periods we're comparing.

The reign of Heraclius, and the seventh century in general, shook the Byzantine state to its core. Through this intensely transformative and destructive period, we see the Roman strategic outlook shifting one final time: to preserve God's empire on earth against the swarming barbarian hordes descending from all directions (from the Byzantine perspective of course).