Nicodemus thought it was about physical birth and was corrected. It is about salvation by God. A spiritual birth from above. Specifically executed by the unique one who has no one like Him...not even among the Godhead. Jesus' physical birth is not being stressed. His uniqueness as a whole is. I think the term "only begotten" leads the reader to focus on the physical nature too much. "Unique one" allows the reader to more freely consider the full being of Christ.You can translate the word as "unique" in either place and not be wrong. The problem for the translator is that monogenes is ambiguous in these contexts. There is no one English word that covers both meanings. Therefore, the translator has to make an exegetical choice.
Again, my exegetical choice of "only begotten" in John 3 is based on the immediate context, which was about birth.
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