No, the East split with the West on doctrine (beginning with the Council of Chalcedon, the specific details of which are unclear to me), and this had an effect on political organization. From about 500 AD onward the Bishop of Rome claimed political power over the temporal authority of kings, although they did not begin actively exercising it until much later. However, in the East, the Church acceded to the notion of co-equality between the emperor and the church. This probably has to do with the restive religious minorities in the East at the time which the Emperor of the East wanted to appease, but I'm not sure.
As for feudalism involving greater centralization, by this I mean that it occurred as the Franks expanded territorial control, and centralized power among the Franks in the hands of one prince. This expansion could only be possible via feudalism. In order to defend against cavalry, the Frankish king exchanged protection and the utilization (but not ownership) of land in exchange for the raising of knights trained as cavalry. In this way the armies raised by the Frankish king would be larger and more powerful, securing more territory for the Franks against their enemies.