A Patriarch, Catholicos or head of sui iurus Church is always addressed by the honorific of Head of Church. Cardinal is only a personal honor bestowed by the Latin Church, it gives certain privileges in the function of the Holy See of Rome and it’s organizational arms.
The title Patriarch, Catholicos, etc as Head and Father of each particular Church is supreme.
It would be proper to refer to the Patriarch named Cardinal as “Your Beatitude” or “Your Eminent Beatitude”.
Also note, Canon 58 of the Code of Canons of Oriental Churches says: “Patriarchs of Eastern Churches precede all bishops of any degree everywhere in the world, with due regard for special norms of precedence established by the Roman Pontiff”
The motu proprio of Paul VI also addresses this:
vatican.va/holy_father/paul_vi/motu_proprio/documents/hf_p-vi_motu-proprio_19650211_ad-purpuratorum_it.html