In Eastern Orthodoxy, is it most important for the efficacy of the sacraments that they be administered canonically by an ordained priest (who is in apostolic succession), or the fact that God is the one who works in and through the Holy Mysteries? Or is it both (or something else)? A discussion of canonical decisions made during the Novation and Donatist controversies would be helpful, as well as the decisions of Church councils. I am specifically interested in the sacraments of Baptism and Holy Communion (the Mystical Supper).
I'm Orthodox, but not a scholar by any means. I can only share how I understand things, and invite correction from the more erudite!
The Sacraments, or Holy Mysteries, are asked from God, for the People of God (Laity), by and with clergy ordained (set apart from among us) to service these needs that we have (baptism, Eucharist, repentance, marriage, healing, burial, etc.); in the context of, and through, the Church (Body of Christ) that we comprise. It is not possible for a person who is not a baptized member of the Church to partake of the Holy Mysteries (sacraments), with few exceptions (which not all Orthodox will even make). In the context of an Orthodox church service, Orthodox Christians, individually and as part of the Body of Christ, offer themselves to Christ, as He did to us, and receive the Mysteries in return. The only question touching on the idea of efficacy, therefore, is whether or not we are making that effort of offering ourselves to God, truly and constantly, and in peace with each other and the world around us, or if we're just taking God's Mercy for granted. Which of course is not to say that you won't get His Mercy, since we can't ever really "deserve" it and there's no way to "earn" it. It's about using your free will to choose to turn toward God and what He wants, instead of turning always to what you want, and accepting what comes from Him in return. I know that doesn't specifically answer the question, but I'm not sure it can be answered in the way it was asked because the frame of reference is quite different. I hope it makes some kind of sense, though!
I'm not Orthodox and I don't know much on Orthodox theology, but I'll try to answer from what I have found.
AFAIK Orthodox Church shares the ex opere operato doctrine though the understanding is not the same (here near the bottom). This means that the answer is "God". The action of the priest is necessary, but not so much, it's less important than in Catholic understanding.
The priest is necessary for Eucharist (like in Catholic Church). For baptism the priest is not necessary: under extraordinary conditions, even a layman can baptise.