I agree the Fall of Rome would be a great time for a civilization collapse. In fact, it could be way worse. If you can get the Sassanids invaded by the steppe tribes and East Rome to collapse with the West, it will take longer for the world to exit the Dark Ages.
If one were to remove the Papacy further, the repository of Roman knowledge and legal precedence may also be weakened or lost for a far longer period of time. Without Christendom in general, the lack of the Papacy and monastic keepers of varied texts and information, would be less likely and the scenario perhaps far worse than otl. Though, I will say that the Roman land systems (manorialism) contributed greatly to the ability for the states of Europe to recover themselves, as at least there was a wider system of land distribution. In the Bronze Age collapse, the migrations seemed far more dramatic and land distribution much less sophisticated and well specified. Though, I am not sure as to the comparison between Akkadian and Latin regarding the ability for these to keep information to the next period of civilizations.
My opinion though, is that the framing of the Akkadian language was certainly 'inferior' in comparison to the Latin of the late Empire as the former had a smaller literate class (no church that covered the majority of Europe and monastic orders) and the the arrival of migrant peoples arrived with less acclimation to the wider Akkadian system than the Germanic peoples had to the Latin world (the Germanic peoples had become associated heavily to the Roman world for centuries already and composed large sections of the Imeprial army and other systems).
There is also the idea that the agriculture was different, with much greater agricultural production possible in the sections of 'Northern Europe' disturbed by the fall. The newer ploughs that revolutionized European agriculture were likely disseminated more widely by the German migrants into the wider Roman world, bringing positives to the rural assortment of Europe. In contrast, the agriculture of the Mid East was less fertile and the migrants likely did not engage in the widespread irrigation needed to maintain larger rural populations in the Mid East. Slavery was another negative factor, we may imagine widespread capture of slaves and their movement across the varied areas in the region after and before the collapse as limiting individual areas in developing more effective populations.
As far as other sections of the world in the fall of Rome and soon after, the Islamic world benefited from having a complex law code and system that restored much order that could have been lost had the conquerors had less. However, the most major negative, was that the Islamic conquest finalized the terminally ill Silk Road, most of which had been accumulating since the fall of the Kushanshah and the rise of large nomadic empires, such as the Rouran and Gokturks. Further, during the early Islamic conquest, certain odd desertification trends extended itself rapidly, especially in Northern Africa, which every decade was weakening in importance. The population of Egypt also seems to have declined during the Islamic period, why, I am not sure of (my opinion tends to be that the decline of the Red Sea trade routes is part of the issue). Iran of course would experience great turbulence in the early Islamic period, various rebellions that would involve decade long wars and conflicts over small areas, already disaffected by the end of the Silk Road and many other negatives.
The desertification also seems to have harmed the southern regions of the Islamic world most heavily. One is reminded of the rapid loss of arable land within Yemen, causing great numbers of Yemeni migrants to the wider Islamic world, especially to Iraq and the fringes. Another region of great disaster was the region of Abyssinia, where the Axumites declined acutely beginning in the 7th century and experienced a slow degeneration in power and population. Meanwhile, evidences seem to show Somali migration into the regions of Ethiopia and this disrupting the Axumite order and assisting in the expanding Islamic civilization narrative. Slave trading also increased in this period as large numbers were acquired by the Islamic warriors on the fringes of the Caliphate. We also see that slavery increased by large pecentages in this period, perhaps a lower rural population and larger urban populations associated with the Abbasid period contributed to this, regardless, the texts indicate that large amounts of slave labor and other imported (otherwise not slaves) labor from Africa, Iran Central Asia and Europe were used in occupations that during the Sassanid period were occupied by free labor, could there have been a smaller rural populace than 300 years prior? My opinion is that this is a correct assumption or at least the best assumption.