The trinity is a very old doctrine. See The Trinitarian Old Testament for just how old. But Nicea (by which I mean the Niceno-Constantinopolitan creed of 381 which we say in church today) gave us certain terminology that is accepted by both East and West. Its creed is basic to all Christian churches. Yet its doctrine of God is a particular one - one that is sometimes unwittingly (sometimes wittingly) side-lined, ignored or opposed.
The first thing to notice is Nicea's doctrine of 'the one God.' To the untrained eye, it looks like it doesn't have one. It simply says 'We believe in one God' and then immediately goes on to speak of 'the Father Almighty', 'one Lord Jesus Christ' and 'the Holy Spirit'. Nicea gives absolutely no definition of the one God except to unfold His being in the description of the Three. No doubt many scholastic theologians (if anachronistically present!) would have inserted quite an extended treatise on the omnis in between "I believe in God..." and "...the Father Almighty". But Nicea doesn't let you force a breach between a description of the One and the Three. To describe the One is to unfold the Three.
When looking for a doctrine of God's 'ousia' (being), again a typical western theologian may be disappointed. All we have in the creed is the controversial phrase 'homo-ousios'. Jesus, the Son, is 'homo-ousion tw patri' (of one being with the Father). There is not here a prior definition of 'ousia' which is then mapped onto the three Persons. Let me repeat: There is not a prior definition of 'ousia' which is then mapped onto the three Persons. Instead we infer what the 'ousia' is from the fact that Father and Son are 'homo-ousios'.
Jesus, in all His difference from the Father, is still homo-ousios with the Father. In His divinity He is 'God from God, Light from Light, True God from True God, begotten not made." Even in His divinity He is 'ek tes ousia tw patri' (out of the being of the Father). There are important differences between Father and Son that are not papered over but rather affirmed by and included in the homo-ousios.
The homo-ousios does not denote three-fold repetition but rather, in TF Torrance's words:
"The Father/Son relationship falls within the one being of God.” (Trinitarian Faith, p119).
Homoousios “meant that the Son and the Father are equally God within the one being of God.” (ibid, p122)
The homo-ousios upholds the distinction (as well as unity) of Father and Son. Remember that you can't be 'homo' with yourself. And it points us to the fact that the Father is Begettor, the Son Begotten. The Father from Himself, the Son from the Father (even according as He is God, contra Calvin but with Nicea!).
There are genuine differences in Persons that in no way compromise their equality of divinity. There is never a time when the Son is not homo-ousios with the Father nor is there a time when the Son is not begotten of His Father. Therefore there is not an ousia of the Father that could ever be separately conceived and then assigned in equal measure to Father, Son and Spirit. Instead the ousia of God is a mutually constituting communion in which Father, Son and Spirit share. The ousia of the trinity consists in three Persons who are 'homo' with one another. While Nicea does not say explicitly that the 'ousia' is the communion of Persons, it points decidedly in this direction. (See Torrance's 'Trinitarian Faith' for more).
All this is to say that distinctions between Father, Son and Spirit are upheld within the divine nature. The divine nature is not a set of pre-determined attributes which are identically mapped onto the Three. The divine nature is constituted by difference, distinction, mutuality, reciprocity - it is a divine life (a dance even!) not a divine stuff.
Compare this with so much doctrine of God in the west. First an ousia of 'omnis' is determined. The one God is discussed for 600 pages in terms of 'uncreated Creator'. And then we face the Three. What do we then do? Simply give to each Person this CV of attributes and insist that this is what the Nicene homo-ousios demanded! On this understanding all difference, distinction, mutuality and reciprocity is banished from the status of deity. In preference to the lively interplay of Father, Son and Spirit, a 'simple' doctrine of the One (read divine simplicity) is forwarded. And God's own being is conceived of as a stuff not a life.
Think I prefer Nicea!