I hear this question a lot, and the simple answer is that, they weren't. But first some background.

The Marian Reforms were not one instantaneous thing, it was a new method of recruitment which was adopted on a case-by-case basis by campaigning senators after Marius came up with the idea. Marius did not establish a true professional army either although the empire was moving in that direction. It was Augustus who truly reformed the army and paid the army out of the Imperial treasury and began standardizing the regiments and how they operated.

The field army as a concept was established in the 3rd century but we don't know exactly when the formalization of the Comitatenses occurred. Formally speaking, the Limitanei themselves aren't even mentioned in Roman law until about 386 when a law in the Theodosian Code actually calls them by that name. Informally, the first Ripenses and Riparienses garrisons on the Rhine were reorganized by Constantine in 312 after he crossed over from Britain. When exactly the centralized Comitatenses began is unknown but the practice started under Gallienus and may have been permanent by Diocletian's reign.

The only reason people think the army of the Principate (27 BC - 284 AD) was better than the army of the Dominate (284-395 AD) is because we're simply taught this myth that everything was decaying and being barbarized. First of all the use of barbarians in the army was nothing new and recruits from as far away as modern Sweden had been in Roman service since the 1st century BC. Second of all the ethnic composition of the army has nothing to do with the quality of the professional regiments. The idea that these peoples were inherently "rowdy" and "undisciplined" to be quite blunt is just outdated 19th century philosophy, loosely based on Roman biases. The majority of the army was still recruited from citizens according to Elton and the typical method of using barbarians in the army was to train and equip them as Roman soldiers and put them into regiments full of Romans, not for them to serve in their own contingents under their own leaders. That happened, but they didn't replace Roman troops, they were allied contingents. At least until the mid-5th century.

Furthermore, the training of the average soldier had not declined since the Principate either. Conscription was now common for the army as well as hereditary service, but it was still by definition a professional army. It just wasn't necessarily a professional volunteer army like the Principate was. Volunteers were still common, actually, but we only have like two examples from literary sources so we can't say how common it was, there's just not enough evidence to make an estimate. Training in the Roman army was absolutely brutal by modern standards. Think back to those old boot camp scenes in movies like Full Metal Jacket, but worse. Practices like decimation, which was rarely used, are barbaric by modern standards. Punishment regularly included things like lashings. But it broke the men. That's something people don't recognize: the Roman army was basically a force of trained serial killers. It had to be, for these men to be able to endure 20 years of service (let alone re-enlist), and they were just as barbaric as the most hardened of their opponents. The drilling and the disciplining to keep them in line was more akin to the brutal techniques used to train fighting dogs than it is modern military drill and discipline, conceptually. It was not a pleasant life, but in some respects it was a better life than what many had before, and combined with not just a guaranteed income, but one in silver or gold, it was extremely attractive. The quality of a recruit coming out in the late Roman period would have been the same as one in the Principate. In fact, he would have been better, equipped with a slightly wider variety of skillsets including basic archery, and trained with more refined and formalized practices than the ones in the principate.

In terms of equipment, the late Roman soldier was also equipped the same or better than his principate counterpart. He still had a helmet, with cheekpieces and usually ear-holes, and a wide field of vision. Underneath his helmet and his armor he would have worn a padded arming cap and padded under-armor, called a Thorocomachus, which absorbed the shock of a blow and added additional protection. Over that he would have worn scale or maille ("chainmail), and so would have the Principate Soldier. Segmentata was still around until about 280 AD, maybe slightly later, but it was never the most common armor, which had always been maille, and Roman-era maille was effectively impenetrable to any handheld weapon except strong bows at close range. Both had a large shield, rectangular during the principate and ovoid or circular after the late 3rd Century, and both had a stabbing sword: the Gladius in the Principate and the Spatha in the late Roman period. But in equipment the late Roman soldier, overall, has a serious advantage. For one, the Spatha is longer, outranging the Gladius, and the Ovoid shield is more maneuverable and better to use in conjunction with the longer blade. He has slightly better coverage with his armor, as his maille has full or half sleeves and extends to the knee, while Principate Maille only extends to the upper thigh or groin, and lacks sleeves. Missile weapons can vary, but typically the late Roman soldier would have been armed with a contus (infantry spear), spiculum (the late Roman pilum), and an array of 5+ throwing darts or light javelins. Roman soldiers in certain parts of the empire also carried more missile weapons as well during the Principate, but we're assuming the standard here, so the single pilum plus the one in the baggage train is all we're going to use.

This question always becomes "who would win in a fight", so who comes out on top? If we constrain every imaginable variable (same quality of leadership, perfectly flat, open terrain, equal numbers, etc. etc.) The answer is probably the late Roman army, and the reason is simple: versatility. The quality of the forces was effectively the same, but late Roman army made more effective use of cavalry and had infantry regiments equipped for engaging any opponent, with more archers, skirmishers, and even the heavy infantry were able to act in these other roles when the need arose. But in reality, the thought experiment is as pointless as the whole "Rome vs Han China" debate. Both armies were suited for the time period in which they fought and adapted themselves further as the empire faced new challenges. The Byzantine period Roman Army improved on the late Roman model for its own unique situation, just like the Dominate army was an improvement on the Principate system.

If you want to read more about the Roman army in late antiquity, Hugh Elton's Warfare in Roman Europe is the standard alongside War in Late Antiquity: A Social History by A.D. Lee.