Two interesting Johannine passages:
John 15.26: But when the Helper comes, whom I will sent to you from the Father, the Spirit of truth, who proceeds from the Father, he will bear witness about me."
John 16.7: Nevertheless, I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Helper will not come to you. But if I go, I will send him to you."
According to Jaroslav Pelikan, who is presumably drawing upon the Orthodox tradition, the sending of the Spirit by the Son is an "economic" reality, while the Spirit's "proceeding" from the Father is an eternal proceeding that does not also flow out of the Son. The East has affirmed the monarchy of the Father as an important element of trinitarian theology. The term "monarchy" probably brings a lot of baggage, but they believe that there is biblical warrant for a unique diversity among the unity of the persons of the Trinity. Jesus himself says in John 14.28, "If you loved me, you would have rejoiced, because I am going to the Father, for the Father is greater than I." In the context of John's gospel, "greater" probably means something more than ontological greatness; I suggest it points to a difference between a greatness that is derivative and a greatness that is non-derivative. This is exactly the kind of difference that the East (and West?) has always affirmed, namely that the Son is eternally begotten of the Father and not the other way around. This similar type of unidirection relationship is then applied to the Spirit's relationship with the Son and the Father. The Spirit proceeds from the Father, and not from the Son. I think this is what the East means by the monarchy of the Father: the Father is the source of both the Son and the Spirit in such a way that maintains their divine unity without eliminated the uniqueness of each relationship. The likes of Gregory of Nazianzus affirmed that John was the first "theologian" because he understood the ultimate genealogy of Jesus, and thus John played a vital role in the trinitarian theology of the 3rd and 4th centuries.
This is a significant case where the Church's reading of Scripture becomes a hermeneutical guide to contemporary biblical interpretation. It is also a reminder that the addition of the filioque clause was, despite the political sins of both sides, an important theological issue: these are not two statements that are essentially saying the same thing.