I realize that both approaches are in need of each other. For a few years I ignored the Brisk method, and focusing all my energy on the calculation of Tosphot. While this in it self seems to me to be highly lacking in today's world, still I see the flaw now--that people when they read my ideas in Talmud will be wondering how do the insights of Reb Naphtali Troup, Reb Chaim relate to the material.
Today this seems to me to be like writing a Ph.D thesis while simultaneously ignoring all previous research into a subject.
If all this seems abstract let me rephrase what I am saying.
You should have the full set of Brisk for reference. That is Chaim Solovietchik' Chidushei HaRambam, Baruch Ber, Shimon Skopf, Rav Eliezer Menachem Shach's Aviezri. [No one has printed Reb Shmuel Berenbaum's classes which would be a fifth addition to Brisk if they were available.] But that does not take the place of calculating the sugia [subject].
While people can be doing the Brisk approach without fully have done the "calculation of the subject," still the calculation does not take the place of Brisk. You really need both.
[This tirade mainly comes from the fact that you find people that can tell over a kind of Brisk idea-sometimes valid, and sometimes not, but is often not related to the actual logic of the sugia at hand. They might know what Reb Chaim says, but not what Tosphot says, or sometimes not even what the Gemara says. ] So now I claim that both Brisk and the more basic type of learning that I usually try to do are both necessary.
I should admit that when I was in Shar Yashu, I did not really grasp what Naphtali Yegear was doing. I saw he was plummeting the the infinite depths of the Talmud and Tosphot, but I certainly had no idea of how to do it myself. And this also goes for later at the Mir. I saw what Shmuel Berenbaum was doing with the "Brisk method." And I think I could have spent time grasping it. But at the time I was gungho (zealous) on learning the basic text of Gemara with Tosphot and the Pnei Yehoshua and Maharsha. It was I think that I wanted understand what earlier achronim [later authorities] were doing with the Gemara before getting involved in Reb Chaim. Today I admit, I very well might have been mistaken. But also you have to understand I was new at the whole thing and simply wanted to get a larger and wider picture of what is flying inside the text. --or maybe I just don't want to admit I wasn't up to the level of the Mir.--and that could be true.