Are there any books that compare and contrast the various methods of Talmud study?
I do not know if you are looking for this (cannot remember a book that discusses this), however I think this might help you.
I would strongly recommend reading the chapter מתודיקת התלמוד by Rabbi Eliezer Berkovitz
Rav Moshe Taragin explains:
I do not assume that there is one method of learning Torah nor that one style is superior to another. Such an assertion would be both arrogant and fatuous. No one would chas ve-shalom minimize the Torah of the Penei Yehoshua or the Maharsha simply because their styles of learning didn't match ours. To learn Torah is to fully appreciate its quintessential infiniteness. By the same token, there has been one distinct style which has popularized itself over the last 100 years and which to a greater or lesser degree is studied in most of contemporary yeshivot - an analytic style which in its purest form is labeled the "Brisker Derekh". This analytic style, which recognizes the fundamental essence of a Health as the source for its constituent halakhic particulars, was by and large practiced by the Rishonim. Indeed, there are different variants of this approach to lamdanut but at their root they all exhibit substantial similarities. It is the aim of these shiurim to explore this methodology.
However, there is an additional hazard to the term methodology. It assumes that within a "derekh" there exists one distinct system and technique for analyzing the gemara and arriving at the desired structure. Such a premise is also erroneous. The nature of intellectual enterprise is that objective knowledge is acquired in a highly subjective and personal manner. I might analyze a 'sugya' from a wholly different perspective than you would even though we would arrive at similar conclusions. There is no specific order or strategy and to adopt one is to stifle the personal initiative which is so vital to true Torah mastery.
One of the מתודיקת of Talmud-study is called the "Brisker method". However:
While the Brisker method has won acceptance in almost all yeshivas today, it has its opponents. These include Rabbi Avraham Yeshayahu Karelitz (1878–1953) (known as the Chazon Ish), who felt that often the existing approach to a Talmudic portion was sufficient. Additionally, the Brisker method is not widely used in modern yeshivas which stem from the Mirrer Yeshiva (originally from Russia), which instead tend to stress single, unifying themes throughout Talmudic concepts, often focusing on only one Rishon if it is seen as the most "truthful" approach to a Talmudic passage
Similary, Rabbi David Samson writes:
The Natziv had a different way of learning Gemmarah which was based upon clarification of the Rishonim method and is explained simply in his book the "Haemek Shela". The Natziv used precise language to clarify if, indeed, this was what the specific Rishon wanted to convey to us. This method is being continued by Yeshivat Mercaz Harav, as prescribed by Rav Tzvi Yehuda Kook zt"l. Rav Kook instructed that one should learn the methodology of the Rishonim and the principle points of the Achronim and then see how they both intertwine and at what point they complete each other.
And on Tosfos:
In order to teach Tosafot one needs to clarify its structure. The Tosafot is broken up into two parts. The first part involves a question, an explanation and three proofs. The second part consists of two proofs and one more unacceptable proof. Thus, the student realizes exactly what he does not understand, which the first step towards understanding is. If the student does not know how to get through this first stage then it will be difficult for him to figure out exactly what he doesn't understand and it will not be easy for him to learn the Gemmarah. However, if the structure of Tosafot is clear to the student and he is able to define to himself which point in the Gemmarrah needs clarification, then that point that he is missing should not detract from understanding that Gemmarah as a whole. The student will then be on his way to understanding what he is not grasping and will be better able to learn Gemmarrah .
Further: see this discussion