Depends which era of Persia we are talking about. The force that flopped in Greece would have lost heavily to the Romans. However, when the Roman Empire reached its zenith, its no coincidence its Eastward push came to a halt at the border of the Persian power at the time - the Parthians. At that point, the two were equals, which is why they spent so much time eyeballing each other until their powers waned and the Arabs exploded out of the desert and pwnt them both. In fact I'm rather surprised to see that the Arab Empire/Caliphate isnt in this poll, seeing as they essentially captured all of the Persian Empire and most of the Romans too.