There is one basic difference between the Yeshivish/Charedi world and Modern Orthodoxy. The difference between the two has nothing to do with being meikil or machmir in halachah or interperting halachah to conform with secular society. It happens to be that many people who claim to be Modern Orthodox are more meikil in an effort to be more like modern society, but that’s not real Modern Orthodoxy. That’s an unfortunate result of what true Modern Orthodoxy was meant to be.
Basically everyone agrees that there are positive and negative things about secular society. The Charedi/Yeshivish world believes that the negative aspects of secular society are too great and therefore we should shut ourselves out to secular society unless it is absolutely necessary. Modern Orthodoxy believes that there is tremendous positive that exists in secular society and we should try our best to take advantage of those positives while keeping away from the negatives. Basically, an ideal Modern Orthox Jew is as shomer Halacha as a Charedi, values Torah as much as a Charedi, but feels a greater involvement in the secular world is a positive thing.
In terms of leaders- I guess the main leaders are the Roshei Yeshiva of YU like R’ Schachter and R’ Willig. Though, to be honest, while the Charedi world in general aren’t machshiv the Rabbanim of the Modern Orthodox world, the ideal Modern Orthodox Jews have tremendous respect and are influenced greatly by the Charedi Gedolim like R’ Elyashiv zatzal and R’ Kanievsky shlita. For example, in YU and many other Modern Orthodox yeshivos and shuls, there were hespedim this year for R’ Scheinberg zatzal, R’ Elyashiv zatzal and R’ Nosson Tzvi zatzal. I am not sure if the main Rabbanim of YU would get that same respect in a Charedi or Yeshivish yeshiva or shul.