Gibbon was writing out of an Enlightenment-era perspective warts and all, it was his firm position that the conversion of the Roman Empire to Christianity is what did it in. Today, historians generally view the crises of the 3rd century (well before Constantine) as the fatal blow to the Empire, which then just stumbled along for the next two centuries before collapsing.
Also, in England in Gibbon’s day there was very little knowledge of or interest in Byzantium. That half of the empire lasted another thousand years in spite of a remarkably tight connection between church and state. Only the Western Empire fell in AD 496.
I've read Gibbon (the abridged version). How would you describe the axe he was grinding?