There are still many ongoing debates about several aspects of the methodology of economic evaluations of health care interventions. Some of the disparities in recommendations on methodological issues may be traced back to different viewpoints on cost-effectiveness analysis (CEA) in general. Two important views are the welfarist approach, which aims at embedding CEA into traditional welfare economics, and the decision maker's approach, which takes a broader and more pragmatic view on CEA. The focus in welfarism may be on utility while that of the decision maker's approach may be considered to be on health. In this paper it is examined how these two views differ and how these differences may subsequently lead to debates in methodological areas. It is indicated that embedding the practical operationalization of CEA in welfare economics seems impossible. In a strict welfarist approach it is necessary to view QALYs as being utilities, although one may question whether such an approach to QALYs is appropriate. Also, equity considerations may play an important role in cost-effectiveness analysis and these should preferably be taken into account in a way that reflects societal attitudes towards an equitable distribution of health care. These equity considerations may not always be directly related to utility or efficiency. Furthermore, both camps may prefer different methods for cost measurement in areas such as productivity costs and informal care. A better recognition of the contents and origins of controversies and disputes may enhance the clarity of discussions.