I understand that the differences may not be that small in this case, but I would like someone more knowledgeable about this subject.
It always seemed to me that the Eastern Roman armies, even during the Macedonian Re-Conquests, were a tad undermanned. Not that Roman Republican armies were that monstruous, but I hardly find any episode comparable to the 86 000 men the Republic fielded in the Battle of Carrhae, or how they kept spamming legions until they defeated Hannibal.
Some people have told me that they were baffled at how Heraclius' Empire was unable to train/field more capable armies after it's defeat in Yarmouk, even up to the point of claiming that the Roman Republic of Scipio would have defeated the first Caliphate and retook the lost Roman Provinces. I get that such an assertion is oversimplifying matters, but then I would like someone more knowledgeable to explain it to me.
What period are you more specifically talking about? You mention the Macedonian reconquests, themes, and the battle of Yarmouk. The Eastern Roman empire in the 6th and 7th centuries had different capabilities and resources to draw from than the empire in the 9th, 10th and 11th. As to why the Macedonian armies were small its simple. The empire only encompassed primarily Anatolia and Greece, smaller population pool to draw from. As for why Heraclius struggled to get more men for his army after Yarmouk, the empire had been through a series of massive crises for a century at that point. The Justinianic plague killed millions and came back every so often depleting the empire's manpower. Simultaneously it destroyed the Roman economy bringing in lower and lower amounts of taxes. Along with this Justinians reconquests ended up being a drain on imperial resources and stretched the military extremely thin all over. During Heraclius' reign itself there had been a war with Sassanid Persia that had nearly destroyed the Romans. The Empire barely had the time to recuperate before the arabs invaded in the 640's. Saying things like the Roman Republican armies could've defeated the arabs is a silly thing to say, its completely unrelated and has no value as a statement. The Roman Republics military was very different than the Byzantines' and had no shortage of manpower. Though it constantly having entire legions annihilated and just pumping out new ones to go and get annihilated again before winning out in the end could not have had a good effect on future Roman demographics.