One difficulty that arises in translating from West to East is the equivocal use of certain terms, the most significant example of which is the use of the term "spirit" to refer both to God's substance and the Third Person of the Trinity, following Tertullian. Because of this, many have accused Western theology of confusing the divine essence with the Third Person of the Trinity, supposedly resulting in the filioque (the Son is co-cause of the Holy Spirit, which completes the essence as it were). I would contend to the contrary that this is simply an account of the Western focus on manifestation in existence, so that this connection between the Spirit and the divine substance simply reflects the connection that I mentioned before between the immanent life (forms) of the Persons and their unique economic modes of manifestation (which are themselves truly God). The action of the Spirit most clearly manifests the spiritual substance of God, as He appears (acts temporally) only as indwelling Spirit. It is this relationship that allows the exegesis of Romans 8:9-11 (particularly "Spirit of God") to take the form that it does, in Marius Victorinus and also in Hilary (De Trin., VIII:21-24).
Consequently, the accusation that the West was following Arian presuppositions in designating the Son as co-cause of the Spirit, such as suggested in Joseph Farrell's translation of Photius's The Mystagogy of the Holy Spirit, won't hold up. The substantia to which the Western Tradition refers is nothing other than the manifestation, the form of God, which DOES proceed from the Father and the Son to the Holy Spirit to complete the unity of the essence. St. Augustine's confusion in De Trinitate was thus well-founded; in fact, the two systems were not referring to the same concepts. Thus, while St. Augustine may have been in error about how the systems corresponded owing to his unfamiliarity with the Greek system (viz., substantia in Latin did not correspond to the Greek hyperousios ousios, nor was subsistentia separable from substantia as understood in the Latin view), his exposition of the Latin view was a true one. It isn't that the concepts were unrelated, but the terms don't match up as Augustine suggested that they did.
In this, St. Maximus Confessor had the best read on the subject, not by proposing a solution, but by having realized the source of the problem:
Those of the Queen of cities (Constantinople) have attacked the synodal letter of the present very holy Pope, not in the case of all the chapters that he has written in it, but only in the case of two of them. One relates to the theology (of the Trinity) and according to this, says 'the Holy Spirit also has his ekporeusis from the Son.' The other deals with the divine incarnation. With regard to the first matter, they (the Romans) have produced the unanimous evidence of the Latin Fathers, and also of Cyril of Alexandria, from the study he made of the gospel of St. John. On the basis of these texts, they have shown that they have not made the Son the cause of the Spirit--they know in fact that the Father is the only cause of the Son and the Spirit, the one by begetting and the other by procession--but that they have manifested the procession through him and have thus shown the unity and identity of the essence. ... In accordance with your request I have asked the Romans to translate what is peculiar to them (the 'also from the Son') in such a way that any obscurities that may result from it will be avoided. But since the practice of writing and sending (the synodal letters) has been observed, I wonder whether they will possibly agree to doing this. It is true, of course, that they cannot reproduce their idea in a language and in words that are foreign to them as they can in their mother-tongue, just as we too cannot do.
St. Maximus here rightly discerns that it will not be a simple case of translation, nor is it even a case that procedere equivocates between two Greek terms (ekporeusis and proienai), which would simply be a case of translating the usage. In point of fact, it lies exactly between the two: the Latin view of substance/essence is something like "immanent energies" or "uncreated glory." The forma is a true and whole expression of the being (substantia) of the Trinity (subsistentia), just as the energeia are said to be God "indivisibly divided." Thus, Rahner's Law requires a modification to be accurate: "The economic Trinity is the immanent Trinity manifested in being."
To be strictly correct, the Latin view says nothing about the source of existence of the Persons qua Persons; it doesn't address the question of aitia or arche at all because it only deals with the Persons as manifested. The Latin view starts from the form and personal acts of the Trinity, using Tertullian's observation that the form (manifestation in being) truly reflects the reality rather than simply being an appearance, and moves from there. Historically, that is the actual Latin view of Ambrose, of Hilary, of Leo the Great, all venerated by the East as Fathers of the Church.
This actually brings us to what is the significant difference between the views: whether this manifestation is according to will or nature. Gregory Palamas follows the patriarch Gregory II of Cyprus in assigning the manifestation of the Holy Spirit in being to the good will (eudokia) of the Father and the Son toward mankind, or in other words, the economy. Tertullian and the Latin Tradition assigns this manifestation to nature, so that the generation of the Son and the Spirit and the distribution of the glory of the form of God are simultaneous (although not necessarily identical) and that both of them indicate that God is homoousion. Obviously, I find this explanation to be entirely in harmony with St. Cyril and the Councils of Ephesus, Chalcedon, and Constantinople. Moreover, I find nothing in Cappadocian teaching that distinguishes the two, since the Latin view does not even address what the Greek Tradition calls the divine essence or the manner in which the hypostases come to possess it. The question of whether the glory of the Godhead manifests naturally by the enhypostasis of the divine essence in the Father or whether it is an act of will seems to be unaddressed in Eastern thought, and accordingly, I see no cause to reject the Fathers (specifically, St. Hilary, St. Ambrose, and St. Leo the Great) in favor of later innovations about uncreated energies being acts of will.