This is a really broad question so the only way I have to answer it is broadly, but, broadly speaking, the Roman imperial center was much more capable of commanding resources than any Medieval kingdom. This is both in terms of armies and things like building projects, as the emperors simply had much more resources to throw around. Now, there are many different ways you could approach this, but I think the biggest difference was the degree of political centralization. If you take the hundred wealthiest and most powerful people in France in 1200 CE, several would certainly be in Paris or in the king's court, but most would be scattered about in the duchies and fiefdoms. In the Roman empire by contrast, every single one would live in the city of Rome or spend significant amounts of time there. And this difference was systemic: a French lord who was growing in power might increase his holdings by quarreling with his neighbors or helping out a nearby lord, important local families on the rise in the empire would move to Rome. Cicero, for example, was the scion of an important family from Arpenum whose family moved to Rome to make their political fortune.

That is why all roads lead to Rome.

Most soldiers during campaigns were levied peasants and farmers.

I'd question this assumption.

See the answers in this thread: https://www.reddit.com/r/AskHistorians/comments/4248f4/if_peasant_conscripts_made_up_the_bulk_of_armies/

Rome, at it's height, could draw on the resources of the entire Mediterranean and Black Sea basins, plus Gaul and Britannia, and in particular the massive grain surplus from Egypt. Just the Roman Army on the Rhine could draw from all of what is now France, something no medieval prince could manage. They had a system that could tax all those areas. They had a logistics system to bring all that to the legions.

See Jonathan P. Roth's The Logistics of the Roman Army at War (264 B.C. - A.D.235)