I have not engaged a lot with the work of Jürgen Habermas (b. 1929), but he is well known for promoting a version of mutual recognition.
At a very preliminary level, it seems he relies more on a presumption of abstract equality between participants, where Brandom incorporates consideration of their actual performance (see Scorekeeping). Habermas has also tended to assume that full consensus is the only desirable outcome, whereas Brandom takes a more positive view of clarifications that do not lead to consensus.
Habermas is a prolific writer, so I may be missing something mitigating, but both these differences seem to me to make the Žižekian criticisms of mutual recognition more applicable to the Habermasian version than to the Brandomian one.