Before I can answer, I must clarify several terms that you are using incorrectly/ambiguously and define how I will approach this question. I also must begin with the disclaimer that I will be answering from an Eastern Orthodox perspective.
Eastern Orthodox vs. Oriental 'Orthodox' vs. Nestorianism
Nestorianism was condemned at the third and fourth ecumenical councils (Ephesus I & Chalcedon I), so calling them 'Orthodox' is incorrect. While some Eastern Orthodox Christians do lump Nestorians and Oriental Orthodox Christians together as monophysite churches, Oriental Orthodox Christians reject this label and distinguish themselves from Nestorians as miaphysite churches.
Concerning Eastern Orthodox and Oriental Orthodox Christians, the difference is that the latter accept only the first three ecumenical councils (Nicaea I, Constantinople I, & Ephesus I), while the former accept seven ecumenical councils. There are some Eastern Orthodox Christians who consider the controversy between Oriental Orthodox and themselves to be primarily semantic (and some dialogue has been made in the 20th century to reunite the churches, but full communion has not yet been restored), but officially they are not considered to be 'Orthodox' (despite their use of the title) as they were condemned as heretical for rejecting the fourth ecumenical council (Chalcedon).
In summary, Eastern Orthodox Christians believe that they are the only Church that can rightly be called 'Orthodox,' and thus Nestorians and Oriental Orthodox Christians are actually heterodox. With that said, I will focus exclusively on defining some key differences between Eastern Orthodox Christians and Western Christians.
Painting Western Christianity With Broad Brush Strokes
Comparing Western Christians only to other Western Christians would be too broad to address in an answer on this site. Similarly, comparing Eastern and Western Christians will necessarily have to be even broader. For this reason, I must make a caricature of Western Christianity that will not fit all Western Christians at all times and in all places. My apologies are extended to those of whom this caricature is not representative. It is also difficult since Western Christianity is extremely divided. For the sake of simplicity, I am lumping Roman Catholicism and Protestantism together (I am aware that many Protestants actually reject this label and consider themselves a separate division altogether, perhaps rightly so in the case of Anglicans - however in this response I will only recognize the two divisions as stated yet treat all of Western Christianity as one group).
Here are some of the primary characteristics of Western Christianity (that stand in sharp distinction from Eastern Orthodox Christian views) that I will use to define it:
- Western Christianity has assimilated much of Hellenistic philosophy/thought. Oddly enough, the opposite charge is often made. However, close study of philosophy and history will reveal that Eastern Christians almost immediately began challenging Hellenistic philosophy and created a distinctly Christian philosophy, while due to historical and linguistic circumstances, much of Hellenistic thought and knowledge of the Greek language was lost in the West for some time and only rediscovered later, and was adopted uncritically by many theologians (cf. Scholasticism). For more information on this, please read Jaroslav Pelikan's outstanding work published through Yale University Press entitled Christianity and Classical Culture: The Metamorphosis of Natural Theology in the Christian Encounter with Hellenism. The implications of this point affect every other point of difference.
- Western Christians believe that mankind has inherited some form of original sin from Adam and Eve that includes an inheritance of guilt. There is a wide spectrum within Western Christianity concerning this issue, but generally it is held that man is depraved to some extent and will go to hell because of 'original sin' if one is not 'saved.' Death is thus viewed as a form of punishment inflicted on mankind because of sin, and 'hell' is a place of intentional, conscience punishment by God (or complete separation from him, which is intended as a punishment).
- Western Christians believe in a juridicial atonement, that is, God's wrath had to be propitiated by a perfect sacrifice: Jesus Christ. Western Christians generally believe that someone has to be punished in order to satisfy divine justice. In other words, mankind deserves to be punished but Jesus gets punished for us.
- Western Christians discuss (forensic) soteriology as an isolated issue within theology (as distinct but related to anthropology, Christology and the theology of the Godhead), and focus on the ordo salutis (which often defines the primary contentions between various Western Christian groups).
I could go on but this will have to suffice (again, this is a broad question).
The Key Differences Between Eastern and Western Christianity
With the above definitions and considerations in mind, I offer the following key differences. This is certainly not an exhaustive list, and they are all interrelated:
Historically, culturally, and linguistically, the two churches have grown apart. The churches grew apart for lots of historical reasons, and the Great Schism was precipitated by numerous factors and made permanent by unfortunate conflicts (namely the Roman Catholic Church's decision to sack Constantinople, the seat of Eastern Orthodox Christianity, during the fourth Crusade). The East continued to mainly speak Greek until the 15th century, while the West soon forgot Greek and spoke mostly Latin and a mixture of other languages (but Latin remained the ecclesiastical language through the Reformation - and it still is within Roman Catholicism).
As previously stated, Western Christianity has assimilated much of Hellenistic philosophy/thought (largely uncritically). Conversely, Eastern Christians went through a long phase of assimilating, challenging, condemning, and modifying Hellenistic thought until a distinctly Christian philosophy emerged (largely attributed to the Cappadocian Fathers). Fr. Alexandre Kalomiros explains this in his speech The River of Fire:
Paganism is ignorance of the true God, an erroneous belief that His
creation is divine, really a god. This god, however, who is Nature, is
impersonal, a blind force, above all personal gods, and is called
Necessity (Ἀνάγκη).... The pagan gods are parts of the world,
and they are immortal because of the immortality of nature which is
their essence. In this pagan mentality, man is also god like the
others, because for the pagans the real man is only his soul, and they
believe that man's soul is immortal in itself, since it is part of the
essence of the universe, which is considered immortal in itself and
self-existent. So man also is god and a measure of all things....
It is this pagan way of thought that was mixed with the Christian
teaching by the various heresies. This is what happened in the West,
too. They began to distinguish not between God and His creation, but
between spirit and matter. They began to think of the soul of man as
of something eternal in itself, and began to consider the condition of
man after death not as a sleep in the hands of God, but as the real
life of man, to which the resurrection of the dead had nothing to add
and even the need of the resurrection was doubtful....
...they began to feel that God was subject to Necessity, to this
rationalistic Necessity which was nothing else but human logic. They
declared Him incapable of coming into contact with inferior beings
like men, because their rationalistic, philosophical conceptions did
not permit it, and it was this belief which was the foundation of the
hesychast disputes; it had already begun with Augustine who
taught that it was not God Who spoke to Moses but an angel instead.
It is in this context of Necessity, which even gods obey, that we must
understand the Western juridical conception of God's justice. It was
necessary for God to punish man's disobedience. It was impossible for
Him to pardon; a superior Necessity demanded vengeance. Even if God
was in reality good and loving, He was not able to act lovingly. He
was obliged to act contrary to His love; the only thing He could do,
in order to save humanity, was to punish His Son in the place of men,
and by this means was Necessity satisfied....
This is the triumph of Hellenistic thought in Christianity. As a
Hellenist, Origen had arrived at the same conclusions. God was a
judge by necessity. He was obliged to punish, to avenge, to send
people to hell. Hell was God's creation. It was a punishment demanded
by justice. This demand of justice was a necessity. God was obliged to
submit to it. He was not permitted to forgive. There was a superior
force, a Necessity which did not permit Him to love unconditionally.
However, Origen was also a Christian and he knew that God was full of
love. How is it possible to acknowledge a loving God Who keeps people
in torment eternally? If God is the cause of hell, by necessity then
there must be an end to it, otherwise we cannot concede that God is
good and loving. This juridical conception of God as a instrument of a
superior, impersonal force or deity named Necessity, leads logically
to apokatastasis, "the restoration of all things and the
destruction of hell," otherwise we must admit that God is cruel....
So the loss of God's grace, which is eternal, spiritual death, in
other words, hell, is in reality an act totally dependent on God. It
is God Who is punishing these people by depriving them of His grace,
by not permitting it to shine upon them. So God is the cause of the
eternal, spiritual death of those who are damned. Damnation is an act
of God, an act of God's justice, an act of necessity or cruelty.
There is far too much that could be said here, so I will allow the quote to stand. I recommend reading the entire speech. Also, I know that the quote hits on a myriad of differences in worldview (which really must be understood before the differences can be understood, as many of the biases inherent in Western Christianity are part of the Western worldview itself), but this will have to suffice for now.
Also, as it stands, I would expect a large number of Western Christian rebuttals to this point. However, please understand that without first studying the underlying thought, it is impossible to have constructive conversation about this (the East and West don't even use terms like 'faith', 'grace', or 'prayer' in the same way/meaning).
The two churches approach theology differently. The East takes an apophatic approach to theology while the West a cataphatic one (this is somewhat of an unfair caricature as both groups take both approaches, and Eastern Orthodox generally balance both ways of doing theology - but again, these are broad caricatures). This represents a fundamental difference in how God may be approached intellectually. In the East, theology begins with the premise that God is unknowable in his essence, but we can encounter him through his energies. It is thus impossible for finite creatures to make cataphatic statements about their infinite Creator. Thus theology is something that the East does, it is not an abstract field of study. The purity of the nous that has been attained by the theologian is vital in the task of theology. Having advanced degrees and knowledge does not make one a theologian, but rather the one who prays is rightly called a theologian in the East, and his or her journey in theosis is directly proportional to his or her ability to 'understand'/'experience' theology, which is an encounter with God himself (as opposed to merely studying a topic; cf. theoria). The West largely approaches theology cataphatically within a Scholastic framework. It would not be fair to deny that the West has had theologians in the Eastern sense of the word, but the West generally labels these individuals as 'mystics,' while in the East all theology is mystical.
The East views salvation as the process of theosis, and thus the Incarnation is the central event in redemptive history. The West views salvation through a multitude of singular events within the ordo salutis, and the crucifixion is generally seen as the central event (although some Protestants would argue that the resurrection is the central event). In Eastern Orthodoxy (as well as in Roman Catholicism and Arminian Protestantism), salvation is synergistic, while in much of (Calvinist-influenced) Protestantism it is monergistic.
The East believes that the central tenet of Western theology is that Western Christianity considers God to be the real cause of all evil - regardless of whether or not Western theologians acknowledge this position or not (some staunch Calvinists admit this). Obviously many Western Christians would disagree. Eastern Orthodox Christians therefore have no need of justifying God (cf. theodicy). In Eastern Orthodoxy, evil is the estrangement from God who is life. Thus death is evil. However, most Western Christians teach that death is a punishment from God, although some Protestants consider death to be 'natural'. Either way, since God is the Creator of all things, the West necessarily believes that God is the real cause of death. They also apply this to the soul, so that God is also the cause of spiritual death for mankind (by punishing mankind in hell). As Fr. Kalamiros explains,
The 'God' of the West is an offended and angry God, full of wrath for
the disobedience of men, who desires in His destructive passion to
torment all humanity unto eternity for their sins, unless He receives
an infinite satisfaction for His offended pride. What is the Western
dogma of salvation? Did not God kill God in order to satisfy His
pride, which the Westerners euphemistically call justice? And is it
not by this infinite satisfaction that He deigns to accept the
salvation of some of us? What is salvation for Western theology? Is it
not salvation from the wrath of God? Do you see, then, that Western
theology teaches that our real danger and our real enemy is our
Creator and God? Salvation, for Westerners, is to be saved from the
hands of God!
Conclusion
This answer is necessarily incomplete. Asking about how the East and West differ in regards to specific doctrines or positions is a much more attainable goal. However, given the broad question, this is my best attempt at answering it. Also, this is certainly a biased answer as it represents an Eastern Orthodox perspective. Obviously a Western answer will differ considerably.
Also, to avoid the duplication of content and repeating myself, I did not address topics that I've answered on before in any depth. You may also wish to check out these responses of mine:
For a great book that explains these differences in greater depth to those already well-versed in Western theology, check out James R. Payton's Light from the Christian East: An Introduction to the Orthodox Tradition.
