since Romans don’t have hesychasm at all, for example.
I wouldn’t say “at all.” There’s quite a lot of overlap between Eastern hesychasm and Western contemplative prayer.
Both Churches are catholic; both are apostolic in origin, and both have seven valid Sacraments (including, of course, Holy Orders, so there’s no concern about invalid Bishops). From a salvation standpoint, there is no difference between the two. Both offer Christian Baptism and Sacramental Confession, so it is possible to have a reasonable expectation of salvation in either Church.
There are many differences in liturgical style, but these are irrelevant to the validity of the rites. There are minor differences among theologians. Eastern theologians, for example, mostly teach that bread/wine becomes Eucharist at the utterance of a particular sentence, while Western theologians usually teach it’s the following sentence. This difference is pretty much irrelevant - it really doesn’t matter exactly
when the transformation takes place, just as long as it happens before the Eucharist is distributed.
The main difference is how each Church views leadership. East and West were united until the Great Schism of 1054. The West continued to recognize a strong central authority (the Pope) who held an Office which was common to all Bishops but with additional authority. This is called Universal Jurisdiction, and the West believes this is a divine charism which is particular to the Bishop of Rome.
The East rejected universal jurisdiction. Their “head Bishop” is the Ecumenical Patriarch of Constantinople. But he is styled as “First Among Equals,” not as a distinctly different type of Bishop. It’s an organizational thing, not a divinely sanctioned thing. Since he is equal to all other Bishops, he has no real authority over any of them.
This is why the Latin Church considers the Orthodox to be schismatics and not heretics. Protestants are heretics (but we’re not supposed to say that these days). Heresy is a dispute over doctrine, while schism is a dispute over leadership.
The thing that mostly divides East and West is our views on leadership, not our views on doctrine.