Okay, first off we must discount any and everything Roman, since Rome is a part of this contest.
Second, good point about the Sassanid's and all that. But the Sassanid's aren't part of this.
Third, you have failed to answer my question. How was Persia a failed state? As far as I am aware, it was thriving until Alexander decided to conquer it. They conquered every other ancient kingdom in the known world, successfully put down Rebellions, were the global source of wealth and knowledge (largely due to Babylon), freed the Jews (again, from Babylon).
Fourth, yes, I am telling you ancient Media, Babylonia, Assyria, etc did not have the road system the Persians built.
Fifth, that you call the Byzantine bureaucracy efficient shows me that you don't know all that much about them. Up through Justinian? Sure. But if we are to judge it as a whole over the entirety of the empire's thousand+ year history, then I will have to say the bureaucracy and structure of the government was one of the primary reasons for Byzantium's malaise.
Look, I'm not trying to knock Byzantium. Their longevity is a huge plus. Constantinople was the greatest city in the world. They somehow staved off attacks on all sides for a long time. They were the religious center for Orthodox Christianity. Lots of pluses.
And yet, the fact that so much of that success is due to Rome and just the natural progression of time and technology brings them down to the level at which I would be comfortable voting for an empire that was utterly destroyed by Alexander over them. Of course they had more written records that survived, because they had several hundred (or thousand) less years to survive than records from the Persians. And paper was more common, and there was a larger literate population. It's just, I need a much more ironclad argument than "lol, Persians were trash because lost to Alexander the Great who also conquered Greece before he conquered Persia" (or, more aptly, put down a rebellion. I forget if he accompanied his father when he conquered them)