The "face to face" interaction of God is through the angel(s), hence there is no contradiction. It doesn't imply Moses directly saw God, he only saw a little glory of God. The angel of God bears the name of God, and he is God himself. The intimacy and detailed nature of the communication makes it as "face to face as a friend". Abraham's interaction was also as direct, however the promise covenant made with Abraham (Gen 15) was unilateral by God alone, which is different from the conditional covenant with Moses as the mediator through angels. Although it can be a midrash intention to choose Angels as the means of the covenant, I believe there has been a tradition that emphasizes that the angels (of God) gave the Torah.
Ibn Ezra on Exodus 3:6:2
AND MOSES HID HIS FACE. This is similar to for I have seen God face, to face, and my life is preserved (Gen. 32:31).58 There too “God” refers to an angel. Jacob implied that there is a great danger in seeing an angel. Similarly, Moses was afraid to look upon an angel.
Ibn Ezra explains the v11 "face to face" in Exodus 3:21:
Moses desired to see the Lord.78Verse 18. God answered him, for man shall not see Me and live (v. 20). This is the truth. For the senses only feel that which is transient. Therefore and they saw the God of Israel (Ex. 24:10), I saw the Lord sitting upon a throne (Is. 6:1), and the prophecies of Ezekiel79 were all visions of God. Look, Scripture here states, and thou shalt see My back. It states elsewhere, and the similitude of the Lord doth he80 behold (Num. 12:8). These things require a long explanation. Saadiah Gaon says that face81In My face shall not be seen (v. 24). refers to the face of the light. Let the face of the sun serve as an example.82 The back83 refers to the remaining light that cleaves to a person.84That is, to the back of the divine light, which a person is able to behold (Weiser). See Saadiah Gaon’s Book Of Beliefs And Opinions, 2:11: “God has a special light which He creates and makes manifest to His prophets in order that they may infer therefrom that it is a prophetic communication emanating from God that they hear. When one of them sees this light, he says: “I have seen the glory of the Lord…” However, when they beheld this light, they were unable to look upon it because of its power and brilliance. Indeed, whoever looked upon it incurred the disintegration of his entire makeup and the flight of his spirit from his body. Moses accordingly asked his Master to give him the strength to look upon this light. The latter, however, answered him that the first rays of this light were so powerful that he would be unable to view them clearly with his naked eyes, lest he perish. He would rather cover him up with a cloud or the like until the first rays of this light had passed, because the greatest strength of every radiant body is contained in its initial approach. All of this was implied in the statement of Scripture: And I…will cover thee with My hand until I have passed by. Then when, the first portion of the light had passed, God removed from Moses the thing that had covered him, so that he might be able to look at the back of the light, as Scripture says: And I will take away My hand, and thou shalt see My back” (Saadiah Gaon, The Book Of Beliefs And Opinion. Translated by Samuel Rosenblatt, Yale University Press, 1948, p. 130). There is no need for all of this.85Saadiah’s interpretation of God’s face and back is wrong. However, before I explain this let me say the following: Know that God only spoke to Moses face to face from the third series of forty days86 onward. Moses’ face shone because God passed by his face. Moses’ prophecy at first was through the angel who appeared in the bush.87. Scripture there states, And the Lord said (Ex. 3:7).88Even though it wasn’t actually the Lord. The same is true of And the Lord went before them (Ex. 13:21),89Even though the reference is to the angel of the Lord. for the messenger speaks in place of the one who sent him.90The angel represents the Lord and delivers His message. Hence God’s angel is referred to as the Lord in Scripture.
Addendum:
As Sommer explains below, this same person of YHWH (the angel of YHWH) is the one who also appeared to and commissioned Moses in Exodus 3.
A further example of this understanding of mal’akh as a humble and incomplete manifestation of Yhwh is found in another JE passage, Exodus 3-4. There we are initially told that a mal’akh appeared to Moses (3.2), but in the remainder of the chapter, it is Yhwh Himself who converses with the shepherd-turned-prophet. The famous fire in this passage, which burned in the bush without burning the bush, is nothing other than a small-scale manifestation of God. 16 This humble manifestation resembles the larger one that would take place at the same mountain not long thereafter, when the Israelites received law at Sinai. (The letter bet in the words, [Exodus 3.2], is the bet essentiae: These words should thus be translated, “Yhwh’s small-scale manifestation appeared to him as [or: in the form of] a flame of fire from the midst of the bush.] – Benjamin D. Sommer, The Bodies of God and the World of Ancient Israel, p. 41-42
Throughout the Exodus account, the angel (“malakh”) of YHWH is continually depicted as YHWH God and yet also as distinct from YHWH God.
An especially revealing case occurs in the J text found in Exodus 33.1-3, which immediately follows the story of the Golden Calf. God, still incensed at the people, announces that He will not accompany the people on the journey, lest He destroy them on the way. Rather, His mal’akh will accompany them. But this mal’akh is not quite independent of God; God uses the first person to describe its activities, not the third (“I shall expel”). The accompanying angel in this passage is the same one JE mentioned in Exodus 23.20-3. There, the people were told they must obey the angel who travels with them because the angel incorporates a manifestation of God’s presence or a hypostasized manifestation of God known as God’s shem (“Name”): “I will now send an angel in front of you…Take care with him and obey him…for My Name is within him”, Exodus 23.20-21). As we shall see in the subsequent chapter, by stating that His name is in the angel Yhwh indicates that the angel carries something of Yhwh’s own essence or self; it is not an entirely separate entity. But it clearly is not fully identical with Yhwh either; after all, the point of the mal’akh in this case is that God will not travel with the people lest the full presence and anger of God destroy them. – Benjamin D. Sommer, The Bodies of God and the World of Ancient Israel, p. 42
In his works, Brown recites observations made by Jewish biblical scholar Nahum Sarna on the same subject Sommer discusses in the quote above.
Nahum M. Sarna – Nahum Mattathias Sarna (March 27, 1923–June 23, 2005) (Hebrew: נחום סרנה) was a modern Biblical scholar who is best known for the study of Genesis and Exodus represented in his Understanding Genesis (1966) and in his contributions to the first two volumes of the JPS Torah Commentary (1989/91). He was also part of the translation team for the Kethuvim section of the Jewish Publication Society's translation of the Bible, known as Tanakh: The Holy Scriptures (The New JPS Translation according to the Traditional Hebrew Text)… He was a lecturer at Gratz College in Philadelphia from 1951 to 1957, a librarian and then associate professor of Bible at the Jewish Theological Seminary, respectively, from 1957 to 1963, and from 1963 to 1965. – wikipedia. org
- According to the Jewish biblical scholar Nahum Sarna, “From several texts it is clear that the demarcation between God and his angel is often blurred [citing examples from Gen. 16:7-9, 11; 22:11-12, 15-18; Exod. 3:2, 4; Judg. 6:11-23]. At the Exodus from Egypt it is now God (Exod. 13:21), now his angel (14:9) who goes ahead of the Israelite camp.” 45, Footnote 45: Nahum Sarna, Genesis, The JPS Torah Commentary (Philadelphia: Jewish Publication Society, 1989), 383 (Excursus 10, Angelology). – Brown, Answering Jewish Objections to Jesus, Volume 2, Theological Objections, p. 27
Addendum 2:
I must copy the excellent answer by user2910 on the Hermeneutics Question Where did the idea that the law was administered through angels come from?:
In many Ancient Near Eastern cultures, there was a political concept we call 'agency'. In this, the delegate or ambassador of a god simply spoke in the first person on that god's behalf. The use of agency is only touched on rarely in the broader historical narrative of Genesis–2 Kings, where we sometimes find the Messenger of YHWH speaking about YHWH in the first person. [For a substantial treatment of this concept as it relates to the Messenger of YHWH, see: René A. López, Identifying the "Angel of the Lord" in the Book of Judges: A Model for Reconsidering the Referent in Other Old Testament Loci] Two occasions where this agency concept are found most explicitly are:
"Behold, I send an angel before you to guard you on the way and to bring you to the place that I have prepared. Pay careful attention to him and obey his voice; do not rebel against him, for he will not pardon your transgression, for my name is in him. But if you carefully obey his voice and do all that I say, then I will be an enemy to your enemies and an adversary to your adversaries." (Exodus 23.20-22, ESV translation)
God's name (authority) is in the angel, and when the angel speaks, it is God's words.
Now the angel of the LORD went up from Gilgal to Bochim. And he said, "I brought you up from Egypt and brought you into the land that I swore to give to your fathers. I said, 'I will never break my covenant with you...'" (Judges 2.1, ESV translation)
The angel speaks, but his words are God's words.
Growing interest in angels
Today's critical scholarship generally agrees that the Genesis–2 Kings narrative was compiled and finalized sometime during or shortly after the Babylonian exile. (Second Kings concludes circa 560 BC.) After the exilic period, during the Second Temple era, we find Jewish literature become increasingly interested in heavenly politics and the role of angels.
This is especially the case in the apocalyptic genre. Whereas the earlier prophets claimed to receive their revelations directly from God ('the word of YHWH came to me', 'thus says YHWH', etc.), the Second Temple literature sees a drastic increase in angelic mediators of these revelations (Zechariah, 1 Enoch, Daniel, to name a few).
It's possible that sometime during this Second Temple period, the growing view that God delegated everything through his angels was read backward into those 'agency' seeds of thought found in the biblical narrative. In this way, readers inferred that God must have revealed the Law through an angelic mediator.
The Book of Jubilees
One such Second Temple text was the Book of Jubilees, a retelling of the Genesis-Exodus narrative written sometime in the second century BC.
It is in this book, perhaps, that we find the earliest references to the idea that God gave the Law to Moses through an angelic mediator:
And [God] said to the angel of the presence, "Write for Moses . . ." (Jubilees 1.27)
And the angel of the presence spoke to Moses according to the word of the Lord, saying, "Write the complete history of the creation, how in six days the Lord God finished all his works and all that he created, and kept Sabbath on the seventh day and hallowed it for all ages . . ." (2.1)
Several more times throughout the book, this angel speaks in the first person:
"I have written in the book of the first law, in that which I have written for you . . ." (6.22)
"For this reason I have written for you in the words of the Law . . ." (30.12)
"All this account I have written for you . . ." (30.21)
"And behold the commandment regarding the Sabbaths — I have written them down for you . . ." (50.6)
". . . as it is written in the tablets, which [God] gave into my hands that I should write out for you the laws of the seasons . . ." (50.13)
