What is meant by asking whether the AV (Authorized Version, that is, King James Version) is more accurate in places? Are you asking whether it is a better translation of the Greek in places?
But then the question arises: “Which Greek?”
The King James Version was translated from Textus Receptus. Erasmus was the author of 5 published editions of Textus Receptus in the years from A.D. 1516 to A.D. 1535. Thus based on this Greek text, the AV translators rendered John 1:18 as:
No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
For “the only begotten Son” the King James translators correctly rendered the Greek phrase
“ὁ μονογενης ὑιος” from Textus Receptus (except the Greek was all in upper-case letters with no punctuation marks).
However, there are two manuscripts prior to 300 A.D. that contain John 1:18.
Papyrus 66, dated about the middle of the second century (around 150 A.D.) has “ὁ μονογενης θεος” (the only begotten God) .
Papyrus 75, dated in the late second century (perhaps around 180 A.D.) has “ὁ μονογενης θεος”. Thus both these manuscripts clearly have “the only begotten God”.
These early dated manuscripts suggest that the apostle John wrote “the only begotten God” in John 1:18. If so, then the King James translators had it wrong, only because they translated from a later Greek manuscript that had it wrong.
So no wonder that the translators of the NASB, considered the pre-300 texts to be correct and thus translated John 1:18 as:
No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained Him.
By the way, Sinaiticus also has “μονογενης θεος” (only-begotten God)
The Son of God, begotten before all ages, was the only begotten God. God the Father was unbegotten.