user15223: Leela Chess Zero is a neural-network based chess engine trained entirely from self play (that's why it has the word "zero" in its name). Leelenstein uses the same binary,* but a different method to train its neural network, utilizing supervised learning.
The latest results indicate that Leela is stronger than Leelenstein. Why?
I'm especially interested in an explanation of why the zero approach is better than the supervised learning approach, if it is indeed superior (presumably it is, or I don't see why Leela would win in the first place).
*As I understand it, NN-engines need two things to operate: the binary file, and the neural network itself. Leela and Leelenstein share the same binary.

user4362: As far as I can see Leelenstein is mostly derivative of Leela. It uses a fraction of the games produced by Leela's self-play to get to a similar playing strength. 
Given that most of these games have also been used to train Leela, there is little reason to expect Leelenstein to be better. 
Basically Leela produces customized trainingsdata via self-play, Leelenstein uses games produced by other engines, which may or may not be consistent with each other.
After self-play Leela uses the data in a supervised fashion. Leelenstein is not a different approach. It's the same approach, only skipping the step of producing its own trainingsdata. 

15223: <p>Leela Chess Zero is a neural-network based chess engine trained entirely from self play (that's why it has the word "zero" in its name). Leelenstein uses the same binary,* but a <a href="https://www.patreon.com/jjosh" rel="nofollow noreferrer">different method</a> to train its neural network, utilizing supervised learning.</p>

<p>The latest results indicate that <a href="https://www.chess.com/computer-chess-championship#event=ccc1217-lc0-vs-leelenstein-finals" rel="nofollow noreferrer">Leela is stronger than Leelenstein</a>. Why?</p>

<p>I'm especially interested in an explanation of why the zero approach is better than the supervised learning approach, if it is indeed superior (presumably it is, or I don't see why Leela would win in the first place).</p>

<p>*As I understand it, NN-engines need two things to operate: the binary file, and the neural network itself. Leela and Leelenstein share the same binary.</p>
 4362: <p>As far as I can see Leelenstein is mostly derivative of Leela. It uses a fraction of the games produced by Leela's self-play to get to a similar playing strength. </p>

<p>Given that most of these games have also been used to train Leela, there is little reason to expect Leelenstein to be better. </p>

<p>Basically Leela produces customized trainingsdata via self-play, Leelenstein uses games produced by other engines, which may or may not be consistent with each other.</p>

<p>After self-play Leela uses the data in a supervised fashion. Leelenstein is not a different approach. It's the same approach, only skipping the step of producing its own trainingsdata. </p>
