I'm have a hard time believing Byzantium survived to 1453. Already a miraculous achievement.
To suppose that it surivived with provinces like Egypt and Syria in its hands, then is to ask us to erase a huge chunk of history - everything from the 7th C. on would be different. The change is too dramatic.
For starters, the above quarrel about west versus east religion are probably beside the point. A Byzantium which had somehow held on to Egypt would be in good course to take Rome, and taking Rome, the Pope, and taking the Pope, the Church. There would be no western church - Catholicism would be as Byzantium defined it. The west might have a disunited collection of regional autocephalus variations, but they would be of no significance and probably wilt in time or fold under Orthodoxy.
This is too dramatic a "what if". The history of the world without an independent pope, or a Muslim conquest, would be a very, very different history.