So I'm 3/4s of the way through binging Mike Duncan's History of Rome podcast and I've noticed a trend I have a hard time understanding. It's often explained that the eastern half of the Roman Empire was much richer than the western half, and that the gap only grew throughout the empire's history. Yet it seems that every civil war was won by the contender from the west. Starting with Octavian defeating Antony, then numerous times in the Crisis of the Third Century (including Aurelian defeating Zenobia), then Licinius beating Maximinus Daia, Constantine beating Licinius and Julian the Apostate beating Constantius II. Maybe the balance shifts after this (I haven't gotten further in the podcast) but it seems strange to me that the side with seemingly more resources always loses. Can this all be chalked up to the abilities of the individual commanders involved, or is there some greater explanation here? Were the Rhine and Danube legions simply that much better than their eastern counterparts?
EDIT: Yes, Vespasian won, but that was after three other western contenders had already duked it out, and Vitellian's guys didn't put up that much of a fight either.
I would say the first major example of Western Roman soldiers, or those stationed in Gaul, Hispania, and Britannia defeating their Eastern counterparts precedes even Octavian and Antony. As the Roman Republic unraveled, Pompey and Julius Caesar faced off in several battles. Pompey had the support of the Senate and most of the resources of the Roman state at that time. Pompey's force certainly outnumbered Caesar's in both infantry and cavalry, but Caesar's hardened veterans of the Gallic Wars were able to persevere after a string of setbacks and finally decisively defeat a much larger Pompeian force at Pharsalus. However, I wouldn't go as far to say that this supports the hypothesis that Western Roman troops were more effective than their Eastern counterparts. In the case of Pompey and Caesar, there are convincing explanations for Caesar's success. Namely Caesar's soldiers were veterans of many difficult years of campaigning in Gaul and utterly devoted to Caesar whereas Pompey's troops lacked experience. Caesar was able to keep his army together after the setback at Dyrrhachium but Pompey and his forces completely lost cohesion when the Battle of Pharsalus started going against them. Pompey also seemed to lack the energy and decisiveness that characterized his earlier campaigns.
As far as Octavian's victory over Antony, the Western legions were barely involved. The battle that won the war was at Actium, a naval battle. Lack of Western Legionary involvement notwithstanding, Actium was a battle largely decided by defections, and also by a large part of Antony's fleet fleeing before they were engaged.
The crisis of the third century is also a mixed bag. While Aurelian did succeed in the reconquest of the Eastern provinces, he did so with what was most likely Illyerian/Dalmatian/Pannonian soldiers as Gaul was busy being a completely separate state: the Gallic Empire. I suppose one could consider the Illyrian Legions Western but the Prefecture of Illyricum sat on either side of the later East-West split post Theodosius I. After Aurelian, Constantius II defeated a Western usurper, Magnentius with most of the military strength of the Eastern provinces. In fact, the Battle of Mursa Major might be the best example of two Roman forces, representative of the military strength of East versus West in a pitched battle. That being said, Magnentius was probably outnumbered by quite a bit so perhaps this wasn't really a fair fight. Before the end of the century, East would prevail over West again at the battle of the Save, where the Eastern (and eventually last Emperor of a united Empire) Emperor, Theodosius I defeated Magnus Maximus.
As far as relative military strength of East and West in the fourth century, we have a few sources that more or less add up to being evenly matched in terms of numbers: somewhere in the 250,000 to 300,000 range for each half. Something that is a bit interesting when reviewing the Notitia Dignatatum is that the Eastern provinces seem to have more garrison units, which makes sense as the population was higher, but fewer units in field armies than the West. The Western Empire certainly had to be more active around the Rhine and Danubian frontiers and was suffering frequent incursions so this makes sense to me. Perhaps this gives the West an edge in terms of number of campaign ready soldiers and combat experience but it's also important to keep in mind this organization was not put into place until Diocletian so the earlier 3rd century Empire might have had a different military strength distribution.
In conclusion, I wouldn't say that Western Roman armies were of better quality than Eastern ones consistently or vice versa. It seems to largely depend on more tactical details like who was leading, the size of the forces involved, and unique developments in the field.
New History, Zosimus
Res Gestae, Ammianus Marcellinus
Notitia Dignitatum
Byzantium and its Army, Warren Treadgold
History of the Decline and Fall of the Roman Empire, Edward Gibbon
Commentarii de Bello Civili, Julius Caesar