There has been some debate over which version of the Bible Eli actually read and carried. I just watched the movie last night, and being a student of the Bible versions issue, I think I can answer.
The first clue we get is when he quotes Psalm 23 to Solara. His quotation is definitely from the old King James Version.
The second clue we get is when Eli and Solara approach Alcatraz island, and he calls out that he has a King James Version of the Bible.
The third clue we get is when Eli begins to recite the entire Bible to the librarian. It sounds like the old King James until the second verse of Genesis 1 when he uses the word "hovered" instead of "moved." This quotation is the New King James Version.
The last clue we get is when the librarian places the finished Bible on the shelf. The binding reads "New King James Version."
The Bible Eli carried was definitely NKJV, not KJV.
If the story were real life, I would account for the contradictory clues by noting that Psalm 23 has been a favorite passage of the church for a long time and is included in many liturgies. As such, the old KJV rendition of it would be more familiar to the memory.
Eli's announcement at Alcatraz that he has a King James Version of the Bible is simple generalization. Unless you have immersed yourself in a study of Bible versions and texts, or happen to be affiliated with the "King James Only" crowd, the NKJV is merely an updated KJV, for all intents and purposes.