The literature suggests that probability weighting and choice set dependence in- fluence risky choices. However, their relative importance remains an open question. We present a joint test that uses binary choices between lotteries provoking Common Consequence and Common Ratio Allais Paradoxes and manipulates their joint payoff distribution. We show non-parametrically that probability weighting and choice set dependence both play a role at describing aggregate choices. To parsimoniously account for heterogeneity, we also estimate a structural model using a finite mixture approach. The model uncovers substantial heterogeneity and classifies subjects into three types: 38% Prospect Theory types whose choices are predominantly driven by probability weighting, 34% Salience Theory types whose choices are predominantly driven by choice set dependence, and 28% Expected Utility Theory types. The model predicts type-specific differences in the frequency of preference reversals out-of-sample, i.e., in choices with a different context than the ones used for estimating the model. Moreover, the out-of-sample predictions indicate that the choice context shapes the influence of choice set dependence.