I'm still not sure. As @Dolores@hexbear.net says it likely had something to do with islamic conquest (not Ottoman though; the split occurred before then). It was against religious law for Sunni muslims to live outside of the House of Islam or to trade with the christians (this rule was of course violated), and their economic and administrative systems took very seperate courses from very early on. Sadly I havent done investigation into exactly what these differences were etc so cannot speak to them beyond generalities such as more centralisation. Deforestation is a strong possibility and definitely a factor, but without more research its hard to know how much

However, drawing on Jones' work on the collapse of Rome, its clear that this divergence between East and West predated the rise of Islam. The trade economy of the West was never as robust as the East, and when it lost imperial trade connections, it collapsed hard, much harder than the East.

In the Eastern empire existing admin anf economic structures were taken over and only slightly altered, existing groups, peasant or aristocrat, taxed. In the West otoh, Rome's settler-colonial policies saw mass settlement of retired soldiers with slaves (from conquests) for farm work. Slaves therefore featured more heavily in the western empire, and as the Western empire fell they rose slightly, to become protoserfs, whereas the remaining free farmers fell into protoserfdom.

These slave-owning small farmers were firmly tied to and dependent on Roman markets for many necessary commodities. As one example, some parts of the empire (e.g. Britain) native-made pottery disappears from the Archaeological record in favour of those imported. As a result, following the collapse, britons had to relearn the ability to make pots from the ground up.