First, there are no more “misnagdim” because we Litvish got used to the Chassidim when the Chassidim calmed down and started learning Gemara like everyone else. Nobody “won” anything.
Second, We Litvish never called ourselves “misnagdim.” That was a label which Chassidim coined in order to differentiate themselves from us. Before two hundred years ago there were no Chassidim. “Litvish” was the mainstream. Chassidism was an innovation by the followers of the Baal Shem Tov, and was regarded with skepticism until it had proven itself kosher and not a cult like Shabtai Tzvi or Frankel’s followers.
Some Chassidic outreach people in their zeal to be mekarev people like to set up an “us lovable Chassidim versus those straightlaced Misnagdim” dichotomy to show that they’re hip and not the old fogeys most non-frum assume Orthodox to be. As one person once tried to tell me: “We [X] Chassidim start with the laws of Simchas Torah and those ‘misnagdim’ start with the laws of Tisha B’Av” in an attempt to show how upbeat he was compared to me 🙂 This attitude is unfortunate, but then again many proper Litvish types I know were mekareved by these Chassidic outreach people, and then moved over to the mainstream when they knew more.
So, there never was a “war” to be “won” in the sense you’re worried about. Eilu v’eilu divrei Elokim Chayim.