In this work, we study different parametrizations of Quantum Decision Theory (QDT) using experimental data made of choices between pairs of lotteries. We then compare QDT with two of most famous "classical" decision theories, Rank-Dependent Utility(RDU) and Cumulative Prospect Theory(CPT). At the aggregate level, assuming homogeneous preferences across subjects, we find that CPT-based QDT wins by far. At the individual level, we classify decision makers as RDU, CPT or QDT. Our major findings are: quantum factor plays a key role in describing subjects’ behaviour; there is a considerable heterogeneity across subjects so that the classic representative agent approach would be completely wrong for this sample.