Which nature of Christ said “My Father is greater than I” (John 14:28)?

If one wishes to know whom the Son is, then the question is, Who is the Father of whom Jesus speaks ?

And the answer is, undoubtedly, the One who spoke from heaven :

And behold a voice from heaven, saying, "This is My beloved Son, in whom I am well pleased." [Matthew 3:17 KJV ]

This voice singled out the individual who had just arisen from the waters of baptism at the hand of John the Baptist, the man prophesied of by both Malachi and Isaiah, as Mark informs us, Mark 1:1,2, who was to go before the face of the Lord, himself, the Messenger of the Covenant.

The one, born of Mary in Bethlehem, who stood on the riverbank, was the Son of the One who spoke from heaven.

And the voice spoke again, to those who had been specifically chosen as apostolic witnesses, who ascended the mountain together with Jesus when Jesus was transfigured, gloriously, before them when he appeared to speak with both Moses and Elijah.

Overawed, Peter, not knowing what he was saying, uttered 'Let us make three tabernacles; one for thee, and one for Moses, and one for Elias'. To which a voice from heaven replied :

And there came a voice out of the cloud, saying, This is my beloved Son: hear him. [Luke 9:35 KJV]

Not on a par with even Moses and Elijah, not to be encapsulated or accommodated with them, This One, Jesus, is the Son of God.

Hear him.

Above all.

And the voice from heaven had spoken once more :

Father, glorify thy name. Then came there a voice from heaven, saying, I have both glorified it, and will glorify it again. [John 12:28 KJV]

Jesus, the One who said, My Father is greater than I, is the Son of the One who spoke three times (a most significant number in scripture) from heaven.

The Father who spoke from heaven had never before spoken in such terms, not either to, or about, Moses or Elijah. This was unprecedented. This is unique.

The Father had never been revealed in this way before. Not as Elohim, nor as Jehovah, nor as Lord. But, the Son on earth and the Father in heaven and a communication between these two Persons, this was a revelation that was further, and far beyond, all previous revelations of Deity.

This is whom Jesus is.

He is the Son of the One who speaks from heaven, as Father.

Obviously Jesus Christ made the statement. This raises the question of what did Jesus mean? Does it mean the Son is inferior to the Father? No, for Philippians 2:5-8 points out that in His preincarnate existence Jesus "thought it not robbery to be equal with God."

What does the statement mean then? In the Incarnation Jesus deliberately subordinated himself. He who had been "in the form of God" took upon himself the "form of a servant" and the "likeness of men." This voluntary humbling did not affect His essential deity.

As one can clearly see the one person of Jesus Christ has two natures, one of Deity on His Father's side and one of humanity on His mother's side. This is one reason that Jesus Christ often referred to Himself as "the Son of God" and as "the Son of Man."

You also ask, "in the Trinity doctrine, who said, “My Father is greater than I?” To get the full "flavor" of John 14:28 you need to read the context of the whole chapter of John 14.

At verses 8-10 Philip ask Jesus to show him the Father. Vs9, Jesus says, "He who has seen Me has seen the Father, and the Father is in Me and I am in the Father." (vs10). In these verses one can see to distinct persons, the Father and the Son.

Moreover, Jesus is not saying that He is the person of the Father. The Father has no separate manifestation from the Son. The Son is the only manifestation and revelation of the Father. What is known of the Father is revealed through the Son. To see the Son is to see the essence of the Father (John 1:1, 18; 10:30; 12;45; Colossians 1:15; Hebrews 1:3).

The bottom line is that Jesus was lesser in position when He incarnated as a man, not lesser in nature. So again, the one person of Jesus Christ who is the only person with two natures was speaking.