EFS advocates are primarily concerned with how the Father, Son and Holy Spirit relate to each other. There is no dispute about their oneness and equality when it comes to essence. The argument rather is that it is possible to identify distinctions in terms of persons and that this distinction includes a form of order. This is because the Father begets the Son and spirates the Spirit.
For Letham, this is seen in the eternal generation of the Son as described in the creeds. He sees this not only in the creedal statements themselves but also in the arguments and writings of key theologians at the time and afterwards. For example, he observes that:
“With Athanasius the doctrine of eternal generation comes into its own. The main issue for him in the Trinitarian crisis is not so much the Son’s being homoousios (of the same being with the Father) but the distinction between created and uncreated.”
Meanwhile Ovey notes that Arianism found obedience/servant language describing Christ in Scripture and used it to prove that The Son was a creature. However, Athanasius noted that fathers did refer to their sons as servants.
“Therefore, Athanasius sees that a natural human father has authority over his son. This authority arises from the paternal relationship. Paternity, therefore has two applications in Athanasius’s argument: first, it allows him to assert identity of nature (humans beget humans), second, it also allows him to explain ‘servant’ language as a consequence of this same relationship.” 
Not only that, but the mark of a bad son as demonstrated by Absalom and Adonijah, was rebellion against their father. 
It is Letham’s view that Eternal Generation does indicate an order in the Godhead although
“Basil opposes any numeration in God, in terms of first, second and third, that would imply difference of rank. Instead we confess the distinction of the persons but hold to the monarchy of the Father.”
This difference no doubt arises from an Eastern approach that sets the monarchy within the Fatherhood, hence the later opposition to the inclusion of the Filioque clause into the creed suggesting that both Father and Son send the Holy Spirit.
However, whilst recognising an order in the Trinity, Letham is deeply uncomfortable with subordination language. He argues that:
“The language of subordination entails that the one subordinated has no choice but is subjected by his superior. The subject of active forms of the verb “to subordinate” subordinates another. This could hardly be the case in the Trinity. It was typical of the Arian heresy. Instead, the use of submission is compatible with an order among the Trinitarian persons and with their equality of status and identity of being. The subject of active forms of the verb ‘to submit’ is a free agent.”
Note that he insists that it is still possible for the Son to submit. Ovey is more comfortable with subordination language but is also clear that the Son is not subordinate in essence but rather, willingly submits out of love.
“Hilary describes the Son’s submission as the “subordination of filial love” (pietatis subjection). Obviously this echoes John 14:31 , where Jesus links his obedience to the father with his love for the Father. Jesus does not seem to consider his obedience demeaning or inconsistent with love.”
For Ovey, the focus is primarily on the love between Father and Son which may appear to be asymmetrical in that the Father loves his son by sending him, showing him his work and giving to him whilst the son loves the Father by submitting to his will and agreeing to the mission plan of salvation.
These points are important because, as representatives of (perhaps the more nuanced end of) EFS and complementarianism, Ovey and Letham are keen to demonstrate a Nicene view of the Trinity with no denial of distinction, unity or equality. At the same time, they also point to the historical texts and controversies around the time of the Council of Nicaea to show that submission and obedience language is possible without denying the Nicaean understanding of the Trinity.
This is important because for Ovey, the idea of humility is essential to love and to godliness so that we might expect to see those things within the relationships that belong to the Godhead if we are expected to imitate them ourselves.
 There has been a long division between Eastern and Western theology with the East preferring to see only the Father as sending the Spirit and the West talking about both Father and Son sending the Spirit.
 Letham, “Eternal Generation in the Church Fathers” pp109 -125 in One God in Three Persons (ed Ware, Bruve and Starke, John. Wheaton, IL.: Crossway, 2015), 112.
 Ovey, “True Sonship – where dignity and submission meet,” pp127 -154 in One God in Three Persons (ed Ware, Bruve and Starke, John. Wheaton, IL.: Crossway, 2015), 142 -143,
 Ovey, “True Sonship,” 142.
 Ovey, “True Sonship,” 144.
 Letham, “Eternal Generation,” 114.
 Letham, “Eternal Generation,” 122.
 Ovey, “True Sonship,” 147.