I'd say either one is acceptable. My Am. Htg. lists them as synonyms.
My own preference would be "effectiveness." For one thing, it's more common.
I'd be more inclined to speak of "degrees of effectiveness" than I would of "degrees of efficacy." I tend to think of efficacy as either existing or not.
That is, I wouldn't say that the efficacy of A is greater than that of B. Perhaps others might.
Edit. Well, Google doesn't show much difference:
"greater efficacy" 168,000 hits
"greater effectiveness" 272,000 hits
"Efficacy" seems to be favored in scientific studies and medical trials, eg., the efficacy of a medicine.
Your example concerns human effectiveness.