Economic research offers two traditional ways of analyzing decision making under risk. One option is to compare the goodness of fit of different decision theories using the samenmodel of stochastic choice. An alternative way is to vary models of stochastic choicencombining them with only one or two decision theories. This paper proposes to look at the bigger picture by comparing different combinations of decision theories and modelsnof stochastic choice. We select a menu of seven popular decision theories and embedneach theory in five models of stochastic choice including tremble, Fechner and randomnutility model. We find that the estimated parameters of decision theories differnsignificantly when theories are combined with different models. Depending on the selected model of stochastic choice we obtain different ranking of decision theories with regard to their goodness of fit to the data. The fit of all analyzed decision theories improves significantly when they are embedded in a Fechner model of heteroscedastic truncated errors (or random utility model in a dynamic decision problem).