The difference was in how the conquered peoples could join up and become full partners regardless of race, ethnicity, location etc. This made a compelling case to flip sides, especially for the wealthy and powerful. They could retain their wealth and position, even get a promotion as a reward for turning traitor early as an example. Just say the shahada, take a Muslim name, and welcome aboard the team. Like the mafia but easier to join. This was very different from the Roman citizen model. Need I go on, really? Is this all new to you? Seriously? Are you just teasing me? Really?
I think you’re a little vague on how the Romans expanded from a tiny city-state in central Italy to control the entire Med Basin and beyond.
Hint: It wasn’t by the original population of Rome growing in numbers rapidly enough to provide the population necessary for the administration and military of such a huge empire.
Instead it was primarily by grudging but steady expansion of citizenship to conquered peoples. They often gave citizenship to leaders of the conquered peoples, especially those who switched sides quickly. By 88 BC all free inhabitants of Italy were Roman citizens.
In fact, by 212 AD all free inhabitants of the empire were citizens. Of course, by that time citizenship didn’t mean much.
They often sped the process up by granting individual citizenship to leaders of the conquered peoples. Julius Caesar scandalized Rome by not only granting citizenship to but inducting Gallic chiefs into the Senate.
My point is simply that Rome was successful in its conquests not because it conquered and held down opponents as Machiavelli claimed, but because it surprisingly quickly turned them into Romans.
BTW, my comment with regard to the graphic you posted was that it implied Islam was so successful in its conquest because it used rape, looting and beheading as tactics. Which implies that other powers of the time did not. Which is of course silly. They all behaved much the same in this regard.
Muslims were so quickly successful primarily because, as you say, they were ready and willing to accept recruits on a close to equal basis. Their taxes, initially, were considerably lower than those of the Byzantine and Persian Empires. And the Muslims offered great religious freedom to their subjects, as least when compared to the policies of the two empires.
IOW, the Muslim conquest was so rapid and thorough simply because the people they conquered saw them as a better deal than what they had, or at minimum not enough worse to cause them to fight desperately in resistance. Conquest was thus a fight against governments, not against peoples. The Byzantines and Persians had arrogantly undermined the foundations of their own empires well before the Muslims showed up.
As it turned out, I think the conquered were mistaken in the long run about Islam being a better deal. But that took centuries to become obvious.