The text in the passages is marked in various ways. If there are differences in the passages (i.e. parts of the text that do no appear in the other passage) those are marked with either red or blue. Variations (i.e. parts of the text that are similar but use different words) are marked in either rose or purple. There are also two quotes of other parts of the Bible in both passages. Those have been marked with green, with a link to the source of the quote after each quote.
|Differences in the text are marked in RED.
Variations in the text are marked in ROSE.
Quotes are highlighted in GREEN.
3 Nephi 20:23-26
23 Behold, I am he of whom Moses spake, saying: A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you. And it shall come to pass that every soul who will not hear that prophet shall be cut off from among the people.[source]
|Differences in the text are marked in BLUE.|
Variations in the text are marked in PURPLE.
Quotes are highlighted in GREEN.
22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you.
23 And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people.[source]
|24 Verily I say unto you, yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have testified of me.
||24 Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days.|
|25 And behold, ye are the children of the prophets; and ye are of the house of Israel; and ye are of the covenant which the Father made with your fathers, saying unto Abraham: And in thy seed shall all the kindreds of the earth be blessed.[source]
||25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.[source]|
|26 The Father having raised me up unto you first, and sent me to bless you in turning away every one of you from his iniquities; and this because ye are the children of the covenant—||26 Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.|
The first thing to note is that the passage in 3 Nephi is not a word for word quote of the passage in Acts. There are some significant differences between the two passages. Let me start with the "God/the Father" variation. In both verse 25 and 26 there are variations where the text in 3 Nephi uses the term "the Father" when referring to God, while the text in Acts uses "God". This may seem like a minor thing but in context it makes sense. In 3 Nephi Jesus always refers to God as "the Father" or "my Father" and thus the difference between the two texts fits with the broader context, i.e. there is no incongruity in the use of "the Father" in 3 Nephi.
Next, in the broader context the inclusion of this passage makes sense, both in Acts and in 3 Nephi, even though their main meaning in their respective contexts are different. In Acts Peter is addressing the Jews and uses the passage to explain to them that they have rejected the prophet that Moses had instructed the Israelites to listen to "in all things". That part of the passage seems to be the emphasis of Peter's larger discourse. But in 3 Nephi the emphasis, despite the very similar language, is on the covenant that "the Father" made with their fathers. Thus the same passage with almost the exact same language has a very different meaning based on the context. In Acts the emphasis is on the prophet rejected, in 3 Nephi the emphasis is on the covenants made.
Finally we can take a look at the two quotes with in the two passages. The second quote, in verse 25, is a quote from Genesis 22:18. There is a slight difference between how the passage in Acts gives the quote from Genesis and the text in 3 Nephi follows the Acts rendering, but there is no substantial difference in the meaning.
The first quote in verse 23 (Acts 3:22-23) is the more interesting one. Even though the passage in 3 Nephi follows almost exactly the wording found in Acts (and not the wording found in Deuteronomy), there is one seemingly minor difference. The "destroyed" in Acts is changed to "cut off" in 3 Nephi. This seemingly minor change is actually very interesting. The King Jame Version of the Bible (the version that Joseph Smith had available to him) uses the word "destroyed", but if Joseph Smith were plagiarizing this passage then why did he change it to "cut off"? It is a minor change, with potentially big implications. The thing is in the versions of the Bible that Joseph Smith had available they all read "destroyed", yet the passage in 3 Nephi uses "cut off". Interestingly many years later when it became popular for scholars/theologians/churches to make their own translations of the Bible this passages frequently got translated as "cut off" (among other things) instead of "destroyed". In other words that one word, "destroyed", in the KJV was at the center of a very minor Bible translation controversy, but it was only years later that revised translations of the Bible changed it from "destroyed" to "cut off". Perhaps they were all taking the lead from Joseph Smith! (not really, but if you want to read more about this then follow this link.)
In the end, if a casual reader happened upon these passages they might think that the version in 3 Nephi was copied from Acts, but a closer reading reveals some rather interesting and important differences that work in context and do not mark the passage as obviously or ignorantly copied to flesh out the text.
Now we can get to the really interesting question. How did it happen that a very similar passage is found in both the New Testament and the Book of Mormon? One response to this is that the both Peter and Jesus were inspired to say very similar words when teaching their respective audiences. This is the response used by some defenders of the Book of Mormon, and this response is used for other passages as well. The general idea is that because God is the ultimate inspiration for the scriptures it should not be that hard for Him to inspire two people on opposite sides of the earth to say or write the exact same thing.
This all assumes that the passage found in Acts originates from Peter. There is no other record of that passage in the Old World before Peter used it in his defense before the Jews, but it is not much of a stretch to think that someone else made a habit of saying something similar before Peter ever used it in his defense to the Jews. It is entirely possible that before Peter ever said it Jesus taught it to his disciples and they in turn taught it to others. When Jesus commanded his disciples to go forth and preach the gospel to all the world, he didn't send his disciples out by saying, "Go tell people some stuff and to do good generally. Oh and make sure you mention me. And baptize, yes baptize people.... That's all." He sent them out with a specific message, in many cases the message was memorized. His disciples spent much of their time with Jesus learning his sayings and learning (memorizing) his major sermons.
There is no indication that what we now know as the four gospels were not written down until at least 30 years after the death and resurrection of Jesus. In the mean time the teachings and saying of Jesus were passed around by oral tradition, meaning people would learn (memorize) the sayings and sermons and would repeat them back to congregations or anyone who bothered to listen. This means that much of what the disciples taught was not original material. In this context it would not be unusual for Peter, when he had to defend himself before the Jews, to reach into his memorized database of sayings and teachings from Jesus and use and adapt a particular saying that Jesus had first taught his disciples. Thus it could be that the passage that is recorded in Acts 3:22-26 was first taught by Jesus and then later was used by Peter.
With this in mind we can return to the passage that appears in 3 Nephi. In this context we have Jesus teaching the Nephites the same things he taught in Jerusalem, so it would make sense that he would include something that he taught to his disciples in Jerusalem, especially Peter. Just because we do not have a record of Jesus teaching it to his disciples does not mean that he did not originate the saying that was later attributed to Peter. This way of thinking about the passages in 3 Nephi and in Acts also shows that when Jesus arrived at Bountiful he continued using the same method of teaching that he had used in his mortal ministry, that of oral tradition. And he made sure that he taught the same things to the Nephites that he had taught to the Jews in Jerusalem. And thus he fulfilled the commandment of the Father.