A heuristic distinction proposed by Theodore De Regnon, which has long outlived its usefulness, is that Greek Trinitarian theology began from the distinction of the divine persons, whereas Latin theology began from the unity of God’s essence. The latter’s preference for moving to trinity from unity makes sense, so the story goes, of why Augustine felt the need to explain the divine persons in terms of a single mind’s interrelated faculties of memory, knowledge, and will.
You only need to read Michel Barnes, Lewis Ayres, Luigi Gioia, or Khaled Anatolios to see that this proposal breaks down very quickly as a reading either of Greek or Latin sources, but a passage from Origen illustrates the absurdity of taking psychological analogies for the Trinity to be distinctly Latin, or even uniquely Augustinian: “We must suppose that as an act of will proceeds from the mind without either cutting off any part of the mind or being separated or divided from it, in some similar fashion the Father has begotten the Son, who is indeed his image” (De principiis 1.2.6, p. 19). Origen uses the analogy for the same reason that Augustine does: the mind, as an immaterial and intellectual substance, is the closest analogue in our human experience to the LORD’s absolute simplicity (cf. Ibid., 1.1.6-7).