Byzantine Empire vs Western Roman Empire

Assume both empires are at their peak (well, can't say that, but lets imagine ).
The West Romans have their Imperial Roman Army

The basic equipment of an imperial foot-soldier was essentially the same as in the manipular Roman army of the Republic: metal armour cuirass, metal helmet, shield and sword.[191] However, specially protective armour - the lorica segmentata and the scutum, a rectangular shield - was developed for legionaries, although apparently not made available to auxiliaries.
Weapons manufacture

In the 2nd century, there is evidence of fabricae (arms factories) inside legionary bases and even in the much smaller auxiliary forts, staffed mainly by the soldiers themselves.[192] But, unlike for the Late Roman army of the 4th century onwards, there is no evidence, literary or archaeological, of fabricae outside military bases and staffed by civilians during the Principate (although their existence cannot be excluded, as no archaeological evidence has been found for the late fabricae either).
Armour

Lorica segmentata: Modern tests have shown that this lorica provided better protection to weapon-blows and missile-strikes than the other types of metal armour commonly used by Roman troops, chain-mail (hamata) or scale (squamata), being virtually impenetrable by ancient weapons. However, historical re-enactors have found replicas of the lorica uncomfortable due to chafing and could only wear them for relatively short periods. It was also more expensive to manufacture and difficult to maintain due to its complex design of separate strips held together by braces and hooks.
The bas-reliefs of Trajan's Column, a monument erected in 113 in Rome to commemorate the conquest of Dacia by Emperor Trajan (r. 97–117), are a key source for Roman military equipment. Auxilia are generally shown wearing, chain-mail or simple leather corslets, and carrying oval shields (clipei). Legionaries are depicted wearing lorica segmentata at all times (whether in combat or in other activities, such as construction) and with curved rectangular shields.[116] But the figures in Trajan's Column are highly stereotyped, in order to distinguish clearly between different types of troops.[193] On another Trajanic monument, the Adamclisi Tropaeum, the lorica segmentata does not appear at all, and legionaries and auxilia alike are depicted wearing either chain-mail or scales. There is general recognition that the Adamclisi monument is a more accurate portrayal of normality, with the segmentata used rarely, maybe only for set-piece battles and parades.[194] It has been suggested that the lorica may have been used by auxiliaries also. But there is no firm evidence for this. Traces of this type of armour have been found in forts in Raetia from a time when no legions were stationed in the province.[195] But these may simply have been left behind by legionaries on temporary detachment. Furthermore auxilia are nowhere depicted wearing such armour.[101]
The provision of more protective and expensive armour to legionaries was probably due to non-military reasons: the army was highlighting their social superiority, just as it did with higher pay. During the 3rd century, when all peregrini were granted citizenship, and therefore legionaries lost their social superiority, the lorica segmentata and the rectangular shield disappeared.[196]
During the 3rd century, the segmentata appears to have been dropped and troops are depicted wearing chain mail (mainly) or scale, the standard armour of the 2nd century auxilia. Officers generally seem to have worn bronze or iron cuirasses, as during the Republic, together with traditional pteruges.[197]
Helmets

In the Julio-Claudian era (30 BC- AD 69), it appears that soldiers continued to use the types of helmet used by the army of the Republic since about 250 BC: the Montefortino-type and Coolus-type. From about 70 CE onwards, these were replaced by more sophisticated designs, the so-called "Imperial Italic" and "Imperial Gallic" types. The aim of these innovations was to increase protection, whilst not obstructing the soldier's senses and mobility.
The "Imperial Gallic"- type which predominated from about AD 70 onwards, is a good illustration. The helmet features hinged cheek-guards covering the largest possible part of the face without restricting the soldier's breathing, sight and shouting-range. A horizontal ridge across the front of the bowl acted both as nose- (and face)-guard and as reinforcement against downward cuts on the bowl. Ear-guards protrude from the side of the helmet, but do not obstruct hearing. A shallow neck-guard was angled to the bowl to prevent chafing against the metal cuirass.
Shields

The legionary scutum (derivation: It. scudo, Sp. escudo, Fr. ecu; Rom. scut), a convex rectangular shield, appeared for the first time in the Augustan era, replacing the oval shield of the army of the Republic. Shields, from examples found at Dura and Nydam, were of vertical plank construction, the planks glued, and faced inside and out with painted leather. The edges of the shield were bound with stitched rawhide, which shrank as it dried improving structural cohesion. It was also lighter than the edging of copper alloy used in earlier Roman shields.[198]
The scutum disappeared during the 3rd century. All troops adopted the auxiliary oval (or sometimes round) shield (clipeus).[199]
Hand weapons

The gladius hispaniensis (adopted by the Romans from an Iberian design, probably during the First Punic War (260-41 BC), was a short (median length: 460 mm) stabbing-sword that was designed for close-quarters fighting. It was standard for the Principate infantry (both legionary and auxiliary). The cavalry used the spatha (It. spada, French épée, Sp. espada, Rom. spada) , a longer (median length: 760 mm) sword that allowed longer reach and easier swing.[51] The Roman Legions also carried a small side arm called a pugio.
Missiles

Legionaries were equipped with the developed version of the pilum, a heavy javelin (throwing-spear) that had been used by Roman soldiers since around 250 BC. This weapon had lead counterweights to assist stability in flight and penetration; a barbed point to prevent withdrawal from flesh or shield; and a buckling shank to prevent it being thrown back. During the Republic, legionaries had been equipped with two of these, but now appear to have carried only one. Modern tests have shown the effective range of these javelins to be about 15m. It appears that auxiliaries were not equipped with a pilum, but with a light spear.
Archers of the imperial army were equipped with the recurved composite bow as their standard. This was a sophisticated, compact and powerful weapon, suitable for mounted and foot archers alike (the cavalry version being more compact than the infantry's).
Clothing

In the 1st and 2nd centuries, a Roman soldier's clothes consisted of a single-piece, short-sleeved tunic whose hem reached the knees and special hob-nailed sandals (caligae). This attire, which left the arms and legs bare, had evolved in a Mediterranean climate and was not suitable for northern Europe in cold weather. In northern Europe, long-sleeved tunics, trousers (bracae), socks (worn inside the caligae) and laced boots were commonly worn in winter from the 1st century. During the 3rd century, these items of clothing became much more widespread, apparently common in Mediterranean provinces also.[200] However, it is likely that in warmer weather, trousers were dispensed with and caligae worn instead of socks and boots.[201]

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Thats a summary of their weapons and all.

Now to the Byzantines (NOT the Komnenians):

They'd practically have the same army as the West, don't they ?

Well, I don't really now much about the Byzantines except that they had Cataprachts! (Actually, I'm trying to learn more about the Romans , trying to get rid of my ignorance on the subject )

So, who'd win ? Who has the better army ?