Late stage western Rome was kinda fine, they even had Christianity kinda receding (Goths and Vandals were far more pious Christians, while in Rome there was plenty of support for restoring the old state religion). What really killed them was intrigue and inability to hold the territory militarily.

Late stage eastern Rome can be divided into a few different long periods. If we mean after being crusaded, then it was shattered and trying to recombine into something useful, eventually finished by Ottomans. If we mean before - well, there was the long period of Seljuk conquest of Anatolia, initially a result of the empire being weakened by conquests against its buffer states and allies which didn't really have to be conquered. But in any case it's probable that the same thing would happen, the Seljuk armies of the initial invasion time are described as quite numerous, and they had a few military innovations east Romans didn't have.