So Western and Eastern Christianity do have fundamentally different metaphysical interpretations of the Trinity which is the actual issue at the heart of the question on the Filioque.
The Western view of the Trinity is like a non-Monarchial form of Modalism, and we see this in the writings of great thinkers like Thomas Aquinas. The Father, Son, and Holy Spirit are mere relations in a single essence/being, often identified as Love itself i.e., the Father generates the Son and their mutual act of love between each other is what spirates the Holy Spirit, he is the act of love between them, thus the entire Trinity itself becomes (or rather is) love (the theology in the west is more positive as opposed to eastern negative theology, so temporal language is often employed) and it is the Trinity by itself that identified as the essence of God. No doubt this understanding of the Trinity has largely been inherited from St. Augustine of Hippo.
The Eastern tradition, on the other hand, is basically the opposite, it's Monarchial Subordinationism (this isn't exactly right but it's the best way to describe it from my point of view). God's essence and his hypostases (what would be considered relations within the essence in the West) are not identified with each other as in the Western Church, so that God isn't necessarily "the Trinity", rather, it is the Father as a hypostasis who, in some sense, alone is God, and it is he who generates the Trinity, for it is he who gives the Son and the Holy Spirit his own essence/ousia that makes both of them God like he is, they do exist distinctly from him, but not outside of him, they exist wholly within him, such a view fully precludes any notion of the Filioque. Now you will see Western theologians speak about the Father as the generator of the Trinity too, but this is due to them inheriting this kind of language from the older Patristics and, once again, they do define this sort of subordinationism in an entirely different way then the Eastern Church does, speaking about it relationally as Aquinas does. I think, however, the way I have defined both, the West being "Non-Monarchial Modalism" and the East being "Monarchial Subordinationism" is really not accurate mainly since I think these terms are much too restrictive anyway and there is a lot of passing back and forth between the two and the area between them is very very grey at times, so take my binary oppositions with a grain of salt.
Now I think this does beg the question though about the Western concept of God, is God, as love, merely an abstraction between the three members, or is it truly something metaphysical? I think this is what largely has given rise the debate centered around social Trinitarianism in the west, taken up by a lot of Protestant theologians in recent years. It seems to me that all the ways theologians have tried to describe the Trinity either come back to God ultimately being the Father or God being an abstract property between the Father, Son, and Holy Spirit. Believe me, there are still debates about how to define the Trinity happening in modern orthodox (orthodox with a small o) Christian circles, all operating off of what was given to us in the Nicene-Constantinopolitan Creed, but all operating off of very different paradigms with distinct histories from each other. Maybe we shouldn't fret on this though, I mean, the Western Church seems to have largely accepted the Eastern view as a valid interpretation of the Trinity alongside its own interpretation, you never really hear the same kind of condemnation from Western theologians on Eastern theology as you will hear Eastern theologians on Western theology, and also the Catholic Church literally gives its Eastern rites the option to omit the Filioque from their Creed and accepts their theology as a legitimate ancient theology alongside its own more scholastic theology of God. Obviously there needs to be limits to our definitions, or that will lead to extreme forms of Subordinationism like Arianism, or extreme forms of Modalism or Monarchism like Sabellianism or Patripassianism, but maybe there are just issues which we cannot fully grasp and have to accept that there may be different ways of defining these things, we are limited in our knowledge after all and will never be able to fully grasp God as he is beyond our reasoning abilities, even the angels don't fully understand God or what he is, and we only know about the Trinity through divine revelation.