This is the 6th and final part of my translation of Rav Itchie Mayer Morgenstern's Kuntres, indentifying many modern movements and Tzadikim in Yiddishkeit with their root sources in Chochma and Bina.
Rav Chaim Brisker and the Chazon Ish:
One can explain the root difference in the difference in Derech Halimud between Rav Chaim Brisker and the Chazon Ish, zy"a, according to the inner essence. (Look deeply and you will find that this explanation fits perfectly in every situation where there is a dispute between them.)
Both Rav Chaim Brisker and the Chazon Ish are considered students of the GR"A. The GR"A was the aspect of Moshiach ben Yosef, who is tied to the sefira of Chochma (as we've explained elsewhere). But the father (Chochma) established the daughter (Malchus), and Rav Chaim Brisker is tied to Chochma in the way that it is Above, and the Chazon Ish is tied to Chochma in the way that it is revealed below, in the aspect of Malchus. And therefore, Rav Chaim Brisker sees every sugya with a completely new vision (since Chochma is the idea of seeing the big picture). And even though Rav Chaim sought depth and straightness of the true pshat (the aspect of the connection of Chochma to Malchus is called Pshat), in his search for Pshat, he has ascended to the root of Malchus, which is Chochma, as we mentioned before.
But the Chazon Ish views Chochma only has it is revealed down below, in the place of Malchus. Therefore, he seeks the most refined Pshat (the aspect of Chochma), but he is exceedingly exacting in the language [of the text he is studying] (the aspect of Malchus). (The Chazon Ish was Mefalpeil in the external things [since external things are discernible, like Bina], but he did not take on the way of Pilpul of building one structure on another and understanding one thing from the other, that is in the aspect of Bina. Rather, he delved deeply into the self-contained Pshat [of what he was studying]. And this is as we mentioned earlier that the light of Chochma is revealed in the place of Malchus.) (Rav Morgenstern, at this point, explained, specifically, many disputes between them [along these lines, but this is not the place to expound on that].
Update: Avakesh has a post which supplements some of these ideas here. It's worth seeing.