Protestants have answered this question in several different ways:

1. That within the Trinity, the Son is eternally subordinate to the Father, though equal with him in essence
2. That Christ here specifically refers to his human nature
3. That the Son is lower than the Father in his role as mediator between God and Man
4. That in his present state of humiliation, he is less glorified than the Father

These views often have some overlap, and many commentators see value in more than one explanation. Baptist John Gill, for example, mentions 1, 2, and 4,¹ and William Burkitt (Church of England) mentions or implies all four.²

Christ as eternally subordinate

The first view is that this passage refers to Christ being, as the second member of the Trinity, eternally subordinate to his Father. Many Protestants reject the idea of eternal subordination, but among those holding to this view are Baptist A. T. Robertson,³ Charles Ellicott (Church of England),⁴ and Heinrich Meyer.⁵ Ellicott writes:

In this passage, as in others of the New Testament, it is plainly asserted that in the divine nature there is a subordination of the Son to the Father.⁴

Robertson agrees, writing that "the filial relation makes this necessary."³ Others, like J. W. McGarvey⁶ (Church of Christ) and Dispensationalist Thomas Constable,⁷ agree with this concept in principle, but do not believe that it is in view in this passage.

Christ on earth

The remaining three positions, though somewhat overlapping and perhaps seemingly similar, are nonetheless considered distinct by a number of theologians. I'll treat them separately, noting where particular theologians seem to overlap.

Christ's human nature

The second view, that Christ is here referring to his human nature being lower than the Father, is not argued by many Protestants, though some attribute it to many of the church fathers. Among the most prominent Protestant proponents of this view are Methodists John Wesley⁸ and Adam Clarke.⁹ With regard to the "greater than I" language, Wesley writes:

As he was man. As God, neither is greater nor less than the other.⁸

Christ as Mediator

This view is perhaps best summarized by the Geneva Study Bible:

Christ is mediator, for in this regard the Father is greater than he, in as much as the person to whom request is made is greater than he that makes the request.¹⁰

It is maintained by Methodist Thomas Coke,¹¹ Philip Schaff¹² (Reformed), the ESV Study Bible, and the Dispensational Moody Bible Commentary. John Calvin, though emphasizing the view we will discuss next, still uses language reminiscent of Christ's mediatorial work:

[Christ] places himself between God and us; and, indeed, as it has not been granted to us to reach the height of God, Christ descended to us, that he might raise us to it.¹³

Christ in the state of humiliation

Among Protestant commentators who clearly prefer one of these positions, this one is the most widely held. These commentators point to the surrounding context, like the New Bible Commentary does:

[This statement] must be regarded in its context, i.e., in the light of the thought that Jesus was going to the Father, which was a process of glorification. His future position would be greater than His present position because of the greatness of the Father.

Constable writes that, due to the incarnation, the Father "enjoyed greater glory than the Son during Jesus' earthly ministry."⁷ As a result, say Jamieson, Fausset, and Brown, the "inferiority of which Christ here speaks [...] would be removed by His going to the Father."¹⁴ Proponents of this view point to two passages in particular: Philippians 2:5–8 and John 17:5:

Christ Jesus, ⁶ who, though he was in the form of God, did not count equality with God a thing to be grasped, ⁷ but emptied himself, by taking the form of a servant, being born in the likeness of men. ⁸ And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross.

And now, Father, glorify me in your own presence with the glory that I had with you before the world existed. [ESV]

John MacArthur¹⁵ and D. A. Carson in particular point to the language of John 17:5 as evidence that Christ here is discussing his return to his full glory, as Carson writes:

If Jesus' disciples truly loved him, they would be glad that he is returning to his Father, for he is returning to the sphere where he belongs, to the glory he had with the Father before the world began (17:5).¹⁶

Others holding this view include the Reformed Study Bible, Presbyterians Calvin¹³ and Albert Barnes,¹⁷ and independents (Church of Christ) James Burton Coffman¹⁸ and McGarvey.⁶ Anglican Leon Morris also defends this view,¹⁹ as does Matthew Poole.²⁰

Summary

While the first of these points is controversial (Christ as eternally subordinate to the Father), Protestants widely agree on the last three points raise here: that through the incarnation Jesus had divine and human natures, that he served as Mediator, and that his time on earth was less glorious than being in heaven. It's thus not surprising that we see all of these views presented as possible explanations for the passage.

However, the most frequently defended view, both historically and especially by recent scholars,²¹ is that Jesus here refers to the Father's exalted position in heaven, a position to which he was about to return.

References and notes:

1. Gill, Exposition of the Whole Bible
2. Burkitt, Expository Notes
3. Robertson, Word Pictures
4. Ellicott, Commentary for English Readers
5. Meyer, Critical and Exegetical Commentary
6. McGarvey, Fourfold Gospel
7. Constable, Notes
8. Wesley, Explanatory Notes
9. Clarke, Commentary
10. Geneva Study Bible
11. Coke, Commentary
12. Schaff, Popular Commentary
13. Calvin, Commentary
14. Jamieson, Fausset, and Brown, Commentary Critical and Explanatory
15. MacArthur, New Testament Commentary, 135–36
16. Carson, Gospel According to John, 508
17. Barnes, Notes
18. Coffman, Commentaries
19. Morris, Gospel According to John, 584–85
20. Poole, Annotations
21. All commentators mentioned above from the last 50 years (Carson, Constable, ESV, MacArthur, Moody, Morris, New Bible, and Reformed) hold to this position, except ESV and Moody.