This paper examines the Bismarckian and Beveridgean-style healthcare systems in 25 OECD countries to identify the relationship between the efficiency of the country's healthcare delivery arrangement and its economic wealth. The Data Envelopment Analysis (DEA) is applied as a quantitative tool. I examine three models using infant mortality and potential years of life lost as output indicators. These models differ only in the way of expressing healthcare inputs. The DEA computations show that neither the Bismarckian nor the Beveridgean healthcare system has a clear advantage over the other when inputs are expressed by health expenditure as a percentage of GDP. The model which uses USD per head expenditure data at purchasing power parity shows a slight advantage of the Beveridge-style systems. This confirms the common opinion that the Bismarck-style systems perform worse in controlling the costs. When inputs are expressed using physical units (medical staff and equipment), DEA shows that the Beveridge system is significantly more efficient than the Bismarckian ones. I analyse the relationship between the DEA scores and the country's GDP per capita, as well. This analysis shows that more developed economies are technically less efficient. These findings are consistent with the belief that technical efficiency is only one of the many criteria that determine the quality of the healthcare system and patient satisfaction.