Kieran Healy, a genuine expert on organ donations, directs me to his 2006 DePaul Law Review article “Do Presumed Consent Laws Raise Organ Procurement Rates?” which concludes that the effect, if any, of opt-out versus opt-in systems is much smaller than I would have thought. In part, this is because countries with de jure opt-out rules still, in practice, tend to allow the next of kind a veto over donation decisions. He concludes that countries like Spain and Italy who’ve substantially increased their organ yields did so not with a quick legal change but because “they have invested effectively in the logistics of the transplant system.”
Much more on this and related topics can no doubt be found in his book, Last Best Gifts: Altruism and the Market for Human Blood and Organs.