I guess what I was going for in my original post was a scenario where Byzantium never really 'got off the ground'. I just picked no-Justinian as an example. (Although as someone pointed out, that might have been a good thing.) The POD I had in mind was not simply Persia/Avars taking Constantinople, but something vaguer, something earlier.
I was imagining an Eastern Empire that was beset from around 400 AD or even earlier with all kinds of bad luck, so much so that they turned inwards and were too busy engaging in civil wars and the like to really arouse Persia's ire. In this scenario, there would still of course be a war here and there with Persia, but nothing like the knock-down-drag-out conflict of OTL that weakened and depopulated both sides so much that they became in effect easy pickings for the Arabs.
What I was thinking about was:
--what are the after-effects on European culture, with no (relatively) strong successor state to the united Roman Empire? Without a continuing Latin presence, is Rome's legacy diluted? Do other cultures gain impetus earlier, maybe so much so that they and not Rome become the cornerstone of later civilization in Europe?
--How does a Persia unweakened by decades of near-constant war look? Does their culture 'catch fire' and become culturally influential in the farther reaches of Europe - the western Med, and the North? Or do they stagnate with no enemy to match their strength, and eventually succumb to somebody else, like the Mongols? Both?
--What happens with Islam?