Obviously, there is a translation error involved, as the two different renderings are incompatible. The question is, which one is right?
Neither ... Nor
The issue is this: Hebrew does not have a dedicated word for "neither" or "nor" as English does. It has the word "not." The text starts with the "and not," then, in poetic fashion, adds the second line of the couplet with "and." Translators get to interpret whether that "and" is disjunctive (joining two unrelated/unconnected thoughts) or conjunctive (linking the two together).
For example, one might say: "I didn't work on Sunday and Monday," and the listener would likely understand that the speaker worked neither on Sunday, nor on Monday. Using the neither-nor expression would be much more clear, but in this case, with only the two words, either expression will likely be correctly understood.
However, with a longer phrase, ambiguity increases. Consider: "I didn't work on Sunday at the time and on Monday." Did the speaker work on just one day of the two, and not on both? Or did the speaker work on neither day? It is now less clear, especially since English has the more clear neither...nor option which was not used.
Hebrew: Not ... And
Hebrew, on the other hand, doesn't have that option. The "neither...nor" structure comes from "not...and."
Here's an example from a different text.
And he brought up Hadassah, that is, Esther, his uncle's daughter:
for she had neither father nor mother, and the maid was fair and beautiful; whom Mordecai, when her father and mother were dead, took
for his own daughter. (Esther 2:7, KJV)
We know that the bolded part should be neither...nor because the same verse says plainly that "her father and mother were dead." However, that "neither...nor" is "not...and" in Hebrew. It could, of course, be translated as "she did not have father and mother," but this is less clear in English--it could mean that she had just one of her parents, not both. But the Hebrew intent is not vague, despite lacking the exact equivalent for the English neither and nor. The "not...and" construction should be clear enough.
Proverbs 30:3
In the verse in question, the "neither...nor" translation is also the best choice. This is for two reasons: 1) the grammatical application explained above; and 2) the poetic parallel of the two lines in this couplet in Hebrew. The word "and" joins two lines which are chiastically parallel.
And neither I learned wisdom
Nor knowledge of the holy have I.
Notice the parallels between "learned" and "knowledge"; and between "wisdom" and "holy." Notice also that "I" comes both early and late in the sequence. This is all part of the typical poetic form in Hebrew, often called a chiastic structure, or a chiasmus. In classic form, one line will be followed by another which repeats back in almost reverse order the same idea but with different words. There are variations where opposites are juxtaposed in this manner, but it is often the case that parallels are made.
The word "one" or "ones" following "holy" is not in the Hebrew, but might be justified by the fact that the word "holy" is plural in form in the Hebrew--like "holies," which would make it seem noun-like, even though it is an adjective.
Conclusion
The KJV translation of this verse renders its Hebrew intent most clearly of the examples provided. The ESV closely follows, though it has added the word "One" to the original text. The translations with "yet" and "but" seem unsupportable, given the Hebrew.
