Aristotelians about causation think all causation is substance causation. Events are causes only derivatively. What does the real causing are substances. This should make Aristotelians very sympathetic to the use of agent causation in the theory of free will. And insofar as the theory of agent causation is just that the agent is the cause of free actions, the Aristotelian who believes that we are substances[note 1] is surely going to agree that we are the causes of our free actions, and we are both agents and substances, so the agent is the cause of her free actions.
So far so good. But there is more to agent causation in regard to free will. Typically, agent causalists invoke agent causation to solve problems such as the randomness problem for libertarians. Agent causation is what makes an action be genuinely one's own action rather than a random blip. But the Aristotelian's embrace of substance causation is too broad. For not only does the Aristotelian think that her free actions are caused by her, she also thinks her non-free actions are caused by her, and even things like the circulation of the blood, which isn't an action at all, are caused by her. Moreover, since she is an agent, she thus thinks all of these things are caused by an agent. But if agent causation metaphysically lumps free actions with non-free ones, and doesn't distinguish them metaphysically from the circulation of the blood, then agent causation can't do the job it's designed for. The Aristotelian believes in agent causation, of course, and may do so with good metaphysical reason, but this agent causation cannot be used to solve the problems that the free will theorists want it to solve.
This line of thought might lead some Aristotelians about causation to accept a version of Cartesian dualism on which we are souls. For then one might hold, contrary to Aristotle, that only our free actions are caused by us and that the circulation of the blood and so on is not caused by us, because we are immaterial beings whose only direct effects are in whatever the equivalent of the pineal gland on this theory will be. This is not in the Aristotelian spirit, though, and it leads to unhappy ethical conclusions (bodies as akin to property).
I think there is something else one should say here. One shouldn't say that agent causation just is causation by an agent. Rather, agent causation is causation by an agent qua agent. You cause your free actions qua agent and you circulate your blood qua mammal, though of course you are both agent and mammal. It is a bit odd to say that you don't perform your non-free actions qua agent, though. After all, how can there be an action without an agent? Aren't all actions, free or not, the actions of an agent qua agent? Maybe. But maybe the distinction is still of some help, for maybe the kinds of mere randomness we want to rule out with the distinction isn't an action at all when looked at more closely.
There is another issue around here. There needs to be more to substance causation than the simple structure substance x causes event E. For paradigmatic substances persist over a long time, but many of their effects happen only at particular times in their existence. And there is an explanation of why the substance causes an effect at one time or another. For instance, I caused oatmeal to be assimilated to me earlier to day because I was hungry. The explanation includes not just the substance, but a state of a substance (and maybe other substances—but that's for another day). I caused the assimilation of my breakfast not only qua agent, but qua hungry agent. Likewise, I circulate the blood not just qua mammal, but qua mammal with a brain stem that sends such-and-such electrical signals to the heart.
Apart from considerations of free will, then, Aristotelians should say that the structure of substance causation is something like: substance x qua in state S causes event E. If we have an Aristotelian constituent ontology, then the state will be a mode (an essence, a necessary accident or a contingent accident) of the substance, and the causation relation will be a ternary relation between the substance, the mode and the event.
But now that we have all of this detail in place, we can go back and ask whether we still get benefits of an agent causal theory in regard to free will. That's not so clear. For instance, when I qua hungry agent caused my breakfast to be assimilated to me, the work distinguishing this from non-actions like circulation is being done by my state of hungry agency. It is because this state is involved in the causation—and not just involved, but involved in the right way (my being a hungry agent could cause me to grow a tail if I was rigged the wrong way)—that I am acting. But event causalists can say something exactly parallel. What distinguishes my eating the breakfast from my circulating the blood is that the former is caused by the event of my being a hungry agent qua my being a hungry agent.
So I do not know that Aristotelian agent causalists can claim to do better than event causalists. In fact, for certain ends they might well want to join cause with the event causalists.