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.
Aristotle explains justice as a kind of proportionality, or equality of relations between people and similar objects of concern. The pseudo-Aristotelian treatise Magna Moralia virtually identifies justice with equality between people, but then disappointingly goes on to say that since, e.g., there is no equality between father and son or master and servant, the concept of a justice between them does not apply. Aristotle himself was careful to point out that empirically existing distinctions between people in the positions of masters and servants do not necessarily reflect inherent ones between people, and this ought to be generalized. Surviving texts do not explicitly put the same caveat on, e.g., existing inequalities between the sexes, but it seems to me the same logic should apply.
It also seems to me that equality of relations between people and similar objects of concern actually implies effective equality between people. A generalized equality between people would have been a highly controversial assertion in Aristotle’s time, and it seems to me he should be commended for implying it, rather than criticized for failing to make it explicit. It is in this spirit that I consider the Kantian emphasis on ethical univerality a welcome addition, complementing rather than conflicting with Aristotle’s highly cultivated sensitivity to the nuances of particular situations.