A couple of useful books:

Peter Brown's "The World of Late Antiquity" is a classic, and IMO, a must-read. However, Chapters XI-XIV are most relevant to the advantages the East had vs. the West.

Michael Grant's "From Rome to Byzantium" is a highly readable book, interspersing the author's own observations with excerpts from primary and secondary sources, though unfortunately a number of the "secondary sources" are from his previous works. Nonetheless, it's a more straightforward parse than Brown, and Chapters 3-6 are directly pertinent to the separate fates of each Empire.

I can also vouch for Warren Treadgold's "A History of Byzantine State and Society" as a useful resource, at least in its early chapters, since it covers the whole history of the Empire. I've read it, but unfortunately don't own it, so I can't give a more detailed rundown of what would be most pertinent to your project.

Good luck.

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