The primary distinction in the Roman Empire was between citizens and non-citizens, and identity was civic-religious and not ethnic in nature. A male Roman citizen from Syria Palaestina was considered more Roman and had more rights than a slave, a freedman or a subject of a client state born in Rome. The bestowal of citizenship to the free people conquered territories was a very important tool for Empire to secure the loyalty the conquered people and to Romanize them from a cultural, religious and linguistic perspective and in 212 AD every single free person in the Empire was made a full citizen as a result of the Constitutio Antoniniana.

I can't speak to societal attitudes of Romans from the Italian peninsula towards their fellow citizens because we don't have much information on that, but from a legal standpoint there wasn't a distinction between Roman citizens from here or there, only between Romans and foreigners.

I don't understand what you mean by the Byzantine Empire having more high-ranking non-Romans? Nearly everyone in the Byzantine Empire was Greek speaking and did not have origins in Italy, but because Romanness was a civic category based on citizenship, they were very much Roman. A Greek speaking free person from Athens or Smyrna (İzmir) or Constantinople (Istanbul) would've called themselves Rhomaion, Roman and not Greek. In fact, when Mehmed the Conqueror took Constantinople and ended the Eastern Roman Empire in 1453, he took the title Kayser-i Rûm, or Caesar of Rome.

---

Sources:

Roman citizenship: a study of its territorial and numerical expansion from the earliest time to the death of Augustus by Charlotte Elizabeth Goodfellow

Citizenship in Historical Perspective by Steven G. Ellis, Guðmundur Hálfdanarson, and Ann Katherine Isaacs

The Impact of Mobility and Migration in the Roman Empire: Proceedings of the Twelfth Workshop of the International Network Impact of Empire by Brill Research Perspectives