[deleted]
Hello!
This is a common question, and I'm sure it's been answered before, but I would be happy to go into detail anyways.
The Late Roman Army is often portrayed as weaker due to modern precepts of "barbarization" (the use of non-Romans) and a particular statement by Vegetius that the Romans had stopped wearing armor. The first is misguided, the second is false. Allow me to elaborate:
The recruitment of non-Romans into the army had always been a part of Roman military policy, at it allowed them to successfully integrate subjected peoples and turn them into Romans. In the Republic they were called Socii, spread throughout Italy. In the late Republic and the Principate, we see the Auxilia, who were non-citizens who received citizenship at the end of their service. With the advent of universal citizenship in the early 3rd century, this assisted in the reorganization of the Roman army over the course of the 3rd century crisis. Beginning in the late 3rd century, we begin to see units of laeti which were peoples settled within the Roman empire who provided recruits for the army. The late 4th century notitia dignitatum (registrar of dignitaries) lists most of them. This system was similar to the other form which is more prominently known - the foederati. Basically these were men recruited by treaty. They were not independent armies and regiments, which the Romans called symmachi or symmakhoi (terminology does get confusing - the Romans did not really standardize it). These foederati were non-Romans thrown into standard regiments with Roman recruits, given full Roman training, equipped as Romans, and treated as Romans. As a result, they were expected to behave and eventually identify as Romans, so when they returned home at the end of their service, they'd contribute to Romanizing their communities and cultures. This practice basically never ended, but a new kind of foederati did emerge in the 5th century. These weren't landed armies, and it's difficult to explain, but basically the 5th century barbarian settlements (based on the research of Walter Goffart) were a more direct form of taxation which was then used to pay the migrant armies, who sometimes would be settled in agri deserti (deserted lands), and who later distorted these agreements to include the land that was being taxed in their payment after the empire began to lose control over the regions they were settled in the 450's AD, which is why each version of this arrangement is different in the different Barbarian 5th-7th century law codes.
The second issue is armor. The Roman army was not uniform, it never had been, although it came far closer to it in some respects than any other pre-modern army ever had or would. First and foremost, Vegetius, the author claiming the Romans had stopped using armor, had no military experience at all. Flavius Vegetius Renatus was probably a Scrinus for the Magister Scrini in the bureaucratic part of the administration, and his knowledge was in veterinary medicine (his mulomedicinae is believed to be his primary work). He wrote some time between the reigns of Valentinian II and Valentinian III, most modern historians saying he wrote for Theodosius the Great or at least probably before the sack of Rome in 410. As a result, his knowledge of the army was based on placeholder units for earmarked political candidates, military parades where soldiers went often without body armor to show off bright and resplendent tunicae superiores (gold tunics), and palace guards or city guards, the former of which rarely wore armor and the latter of which weren't given it in their funding since the capital cities of Italy weren't under threat (yet).
The majority of the army, however, wore armor. The late 6th century Strategikon states that at least half of the infantry and cavalry should have a hauberk and a helmet, and file leaders should have greaves (calf armor). Finds of armor from the 5th century are rare but from the late 4th century include examples of Scale and Maille (chainmail) from Trier, Maille from Weiler La Tour, and the Maille fragments from Sarry might be 5th century. Helmets are more abundant, including 5th century finds from Concesti (Imperial Gift to a Hun), a field near lake Venlo (unprovenanced, poor reconstruction, but probably authentic), and Iatrus (wiped out by the Huns in 443 or 447). Roman arms factories were continuing to produce standardized military equipment until the breakdown of the west, and then the army shifted to newer styles of equipment (from ridge helmets to banded and spangenhelmets, as well as the elaborate Roman Baldenheim). Standardized equipment from arms manufacturing centers would continue to be produced into at least the Komnenian era (my knowledge of the later Byzantine military is a bit fuzzy). The Principate Army hadn't been much different. We don't know how much armor they used, but the Strategikon indicates it was also at least 50%. The difference was that there were more occasions where the army needed more mobility, and left its armor in the baggage train or at camp, because the Roman army had become far more versatile.
As for military effectiveness: Hugh Elton claims the Roman Army never lost a major military set-piece battle in the 5th century. This isn't true, the Romans were badly defeated by Attila the Hun at the Battle of the River Utus and the Battle of the Chersonese in 447, and at Calama by Gaiseric in 430, again by Gaiseric in 431, by Theodoric the Visigoth at Tolosa in 439, and by the Suebes in 446. Despite this, Roman military success certainly vastly outweighed their failures in the first half of the 5th century. Almost all of Flavius Stilicho, Flavius Constantius III, and Flavius Aetius' engagements ended in military success. However, it should be noted that while Aetius achieved the most success, he was also primarily an ambush commander and was working with dwindling resources. But the Roman army certainly maintained significant advantages in training and equipment, and saw remarkable success. What ultimately undermined this was of course Gaiseric's taking of North Africa, the primary Roman economic base, which resulted in a down ward spiral of tax cuts, reduction of the military, and territory loss.
The 4th century didn't have these problems. Roman units were smaller, and were undergoing a constant era of transition that had began in the early 3rd century from the Principate Army to the army of Maurice and the Strategikon in the late 6th, but was highly effective. Emperors like Constantine and Constantius II successfully attacked deep into Dacia and Germania, defeating hostile tribes and shuffling the friendly ones towards the frontiers. Julian II campaigned deep into Persia, but was ultimately killed in an ambush. Roman military failure was usually the result of poor leadership, like Valens at Adrianople. In the 5th century it was usually the result of exploitation of weakness, like during the civil wars between Aetius and Bonifatius, or when allies deserted like the Goths did in 446. But the army itself wasn't weaker.
Sources:
(This answers your first question, second question coming up. There's a word limit).