I can give you some summaries of the derech halimudim of the popular rosh yeshiva:
Rav Hershel Schachter: he explains the basis and shittos of the tanaim, amoraim, etc. For example, he would say there’s a machlokes between tosfos and the rambam on how to understand what a niddah is. The rambam says a niddah is an arvuh, tosfos says a niddah is not an arvuh. Where does tosfos get his opinion from? He would then proceed to take you on “the tour of shas” and answer up all difficulties as such.
Rav Mordachai Willig: I’m not as familiar with his style, but he is very halachick. He learns the mishna, gemara, rishonim, achronim, then shulchan aruch, pointing along chiddushim on the way. My friend once described his shiur as the whole thing being chiddushim.
Rav Rozenswieg: Brisk like no other
But you can see for yourself on YUTorah.org