Part because this was the wotd a couple of days ago and part by request for the comparison to effective, I finally have time to think about how these words relate.
Well, it turns out, I don't have to think to hard. Efficacious comes from the Latin "ef", a derivative of "ex" for "out" and "facere" for "to do or make", meaning poetically, to bring about and effective comes from the same Latin origin. Thus, the etymology of effective is consistent with the current usage. So, the only difference is the second adjectival ending on effective making it into efficacious is, as we learned in "robustious", that the second adjectival ending makes the original adjective into "possessing the qualities of" whatever the original adjective was. As I described then, it is adjective-lite.
So, in practice, lawmakers aspire to make effective law, but only end up with efficacious law until it is overturned by the Court. Yes, and true. Efficacious medicines are good enough so that the manufacturers won't get sued, but not effective enough to actually cure the disease since there's no market for that. Yes, and cynically true. Telling the younger brother to stop hitting his older sister as they were driving cross-country was efficacious in short bursts, but playing the on-board DVD on "The Little Mermaid" was effective to stop not only the fight, but all whining, questions and other noises from the back seat. Yes, and it's a good movie. Plaintiff's counsel's oppositions to my motions for summary judgment are only ever efficacious. Plaintiff's counsel's themselves are never really effective. Do I need to state my position on this?
Therefore, I would tend to make effective use of effective, and save efficacious when I want to make fun of something that should have been effective.