While it's true that the churches in Rome and Constantinople were different before the Great Schism, they weren't that different for the first few hundred years. Their differences grew and accelerated from the late 5th century onwards. However, our perception of their differences is heightened by the tendency to view these two churches as poles and so to polarise the differences between them.

Antioch was a major population center in most of Late Antiquity, with close imperial ties, and a thoroughly Hellenised culture. Every evidence suggests that it was not significantly distinct from what we think of as the Constantinopolitan church.

As for Jerusalem, it's identity as one of the 5 patriarchal sees was mostly because of the historical prestige of the city in connection with Jesus and Christianity's Jewish origins. But the indigenous Christian community fled the destruction of Jerusalem in 70AD, and the town was rebuilt as a Roman one. When Hadrian rebuilt it as Aelia Capitolina, both Jewish and Christian presence was forbidden though post-Hadrian this was relaxed as far as Christians go. In late antiquity, under Constantine (and onwards), Jerusalem flourishes with imperial support and church life there flourishes. But it's very much in the Byzantine mold. So again, not that huge a difference from Constantinople.

Alexandria is probably the biggest 'different' church from Constantinople, and from Rome. It's history as a major city predates Christianity, it develops as an early centre of Christianity independently of Rome (and of Constantinople, being a major Christian centre much earlier), and it preserves unique features of Hellenic Christianity in its Egyptian context. Alexandria preserved a more collegiate view of its bishop than a monarchic one for much longer than any other city. It was more 'Greek' in its outlook, but allied itself with Rome more often than any other centre (I'm thinking of in the 4th century theological debates in particular), and acted something like a '3rd power' to Rome and Constantinople.

So, in summary, Antioch and Jerusalem, probably not that distinct. Alexandria, more distinct. Rome and Constantinople? Mostly distinct because we polarise them so much.

Great question! It's hard to provide a clear-cut answer and I will not be able to provide you with a detailed summary of their precise liturgical/doctrinal differences, but I hope my sketch of the five patriarchs before and during the seventh century would prove to be interesting for you nonetheless (in addition to /u/talondearg's answer).

There is a vast range of issues that I could talk about, but what I know best is the fallout of the Council of Chalcedon in 451, which, to make a long story short, was a dispute between Chalcedonians (those who followed the teachings eventually agreed at the council) and miaphysite Christians, those who did not. The precise theological implications need not bother us here, but suffice it to say that many eastern bishops were sympathetic to the miaphysite course, even though the Council ultimately decided against their doctrine. This had major implications for all five patriarchates - for Jerusalem, it was important simply because it was given the same pride of place as the other important sees at Chalcedon. The papacy in Rome had meanwhile weighed into the debate with the Tome of Leo (the work of Pope Leo the Great), which annoyed miaphysite-minded churchmen in Egypt and other eastern provinces, who thought that it was dangerously similar to 'Nestorianism', a major 'heresy' condemned at the earlier Council of Ephesus in 431. On the other hand, the patriarchate of Constantinople was recognised as second only to Rome in honour, a distinction that would continue to impact on east-west relations for centuries afterwards. The reception in the provinces was the most tumultuous, most notably when the Chalcedonian patriarch of Alexandria was murdered in 457, but unrest also took place in Jerusalem. From then onwards, both miaphysite and Chalcedonian candidates jostled for control of the patriarchate of Alexandria (including such wonderful characters as Timothy the Cat and Timothy Wobbly-Hat), so at this early stage we can already see a sense of difference with other churches over this crucial issue.

Yet this can also be interpreted as evidence that the five patriarchates were still functioning in a similar world - different factions were after all fighting for influence within the same system. Yes, miaphysitism is now the position held only by non-Chalcedonian churches (aka not Roman Catholicism and Eastern Orthodoxy), but at the time it was far from clear that miaphysites would not ultimately be the winner of these disputes. In 482, Emperor Zeno had issued the Henotikon, which was essentially a compromise document intended to bring about ecclesiastical harmony in the east - but at the price of costing support in the western church, which saw any compromise on Chalcedon as unacceptable. This continued under his successor, Anastasius (491-518), who was an outright miaphysite sympathiser. Even then, church politics remained complex, for some miaphysites and Chalcedonians were willing to be in communion with each other by following the Henotikon, whilst hardliners on both sides refused to budge. In all the four eastern patriarchates therefore their views shifted backwards and forwards; rather than a sign of difference, I prefer to see it as all factions engaging with their opponents within an imperial framework. Miaphysite Alexandria for instance might be out of communion with Chalcedonian Antioch, but that did not mean that they were distinct churches, for both sees in the early sixth century also professed beliefs in the Henotikon and thus the official position of the imperial church. Unfortunately this period is rather complicated and we can't really generalise it one way or the other!

In 512, the miaphysite faction seized control of Antioch at a time when Anastasius was growing bolder in his sympathies for their cause, yet events elsewhere continued to thwart their efforts. Major riots in Constantinople and a revolt in Thrace broke out over the emperor's policy, ensuring that neither the capital nor Jerusalem could be won for non-Chalcedonians. In 518, with Anastasius' death and the accession of a Chalcedonian emperor, Justin II, the table was turned. Constantinople finally rejoined communion with Rome (after the Acacian Schism that began over the Henotikon), whilst many miaphysite bishops were removed from office across the eastern provinces (though they held onto Egypt for a bit longer). It is perhaps at this time that we can began to discern the origins of a new miaphysite church, but they had not yet developed a parallel structure yet. When we speak now of the patriarchs of Alexandria, Antioch, and Jerusalem, they were now all Chalcedonian, just like Constantinople and Rome. Moreover, despite their Chalcedonian pedigree, Justin and his nephew, Justinian, also pursued reconciliation with miaphysite groups, a policy that would be the hallmark of imperial policy for the next century. There were many examples of persecutions, but there were also periods of intensive negotiation, so again it is not so clear that the eastern churches had truly become separate from the 'mainstream' of the imperial church.

It was only in the 540s that Syrian miaphysites began to cautiously construct their own church hierarchy and later still for those in Egypt; even then, these efforts also took place alongside various deals with the imperial government, or were themselves disrupted by miaphysite infighting. By the late sixth century, we can finally speak of miaphysite patriarchs in Alexandria and Antioch, but it is hard to estimate their popularity or whether they were in any position to replace their Chalcedonian counterparts. This is where it gets confusing, since there were now generally two patriarchs of Alexandria/Antioch, both of whom would naturally have proclaimed themselves to be utterly 'orthodox'. I'm not so familiar with the miaphysite sources, so I can't talk much about them in this period, but the Chalcedonian bishops were very much in tune with bishops elsewhere, even the pope in Rome. We know, for instance, that Eulogius of Alexandria, John the Faster of Constantinople, and Anastasius of Antioch were good friends with Gregory the Great, and that the pope had at least communicated with the patriarchate of Jerusalem. As the recent Brill Companion to Gregory the Great has put it, these men formed a circle of elite churchmen, with similar backgrounds and friends. They simply could not be studied in isolation and it is important to recognise that they would have themselves saw each other as brothers within the same church. The 'official' patriarchs then were very much united in their beliefs and sentiments, a rare event in late antiquity!

Things got a lot more messier in the seventh century, but also, I think, rather more interesting. The war against Persia in 603-628 profoundly damaged the empire and Emperor Heraclius (610-641) embarked on a grand ecumenical project to shore up his support in his church by negotiating with miaphysites and even 'Nestorians'. Contrary to what you might read elsewhere, recent scholarship has emphatically demonstrated this initiative's success. By shifting the focus onto monenergism and monotheletism instead (rather than Chalcedonianism/miaphysitism; again I'm glossing over the theological nuances), even Egyptian monks, often the most recalcitrant miaphysite activists of the previous century, rejoined the imperial communion. A parallel miaphysite church still existed throughout the east, but for a brief moment in the 630s, it looked as though the Chalcedonian-miaphysite divide would finally be healed. That was not to be and even before then hardliners were beginning to agitate - although all the Chalcedonian patriarchs ultimately agreed with the imperial policy of reconciliation, Sophronius of Jerusalem was an early voice against it. His friends continued his cause after the fall of Jerusalem, a campaign facilitated by events, for Cyrus of Alexandria, a prominent monothelete patriarch, was first exiled for political reasons and then had his reputation ruined by negotiating the surrender of Egypt to the Arabs. The ecumenical spirit of the 630s soon disappeared, replaced with a firmer sense of difference. This is why in miaphysite histories of this period the Romans/Byzantines emerge as great persecutors of the faithful, rather than negotiating partners of a grand doctrinal union.

Yet important continuities still remained. The Chalcedonian (and monothelete) patriarch of Antioch, exiled after the loss of his city to the Arabs, seemingly dwelt in Constantinople until 680/1, where he emerged as a great defender of this compromise formulation. Unfortunately for poor Macarius, the Council of Constantinople held then actually repudiated monotheletism, which led to Macarius being sent to Rome to be 're-educated' by the firmly Chalcedonian papacy. But this sad story is telling nonetheless, for evidently Antioch was still represented at an ecumenical council and was still part of the world surveyed by the bishops of Rome and Constantinople. The same was true for the other eastern churches, as Chalcedonian churchmen continued to venture into the empire, albeit in smaller numbers, to attend councils.

The Chalcedonian church in the caliphate however was a declining force, for the miaphysites were rising to the fore under Arab rule, perhaps because of their lack of connection with Constantinople. The Chalcedonians became known as the 'Melkites', meaning 'royal', a reference to their imperial links, and became the minority whether in Egypt, Palestine or Syria, whilst the miaphysite churches continued to thrive, in time developing into the modern Egyptian Coptic and Syrian Orthodox Churches (amongst others). In short, whilst there were important doctrinal differences, they were not irreconcilable and were regularly bridged via imperial compromises. These churches now look very different, but a seventh-century observer would, I think, see things differently.