This study compared attribute- and alternative-wise mechanisms in intertemporal choice. The trade-off (Scholten, Read, & Sanborn, 2014) and the proportional difference models (González-Vallejo, 2002) were used to represent the attribute-wise mechanism. A stochastic version of the hyperbolic model based on Rachlin (2006) was adopted to represent the alternative-wise mechanism. Three experiments were performed. In Experiment 1, a typical intertemporal indifference choice task with a fixed delayed amount was used. In Experiment 2, a general choice task with nonimmediate delays and varied attribute values was employed. The magnitude effect was embedded in this experiment. In Experiment 3, the models were tested with option sets designed to induce subadditive and superadditive choice patterns (Scholten & Read, 2006, 2010). In Experiment 1, the hyperbolic model performed as well as the other models. In Experiments 2 and 3, the attribute-wise models outperformed the alternative-wise model in terms of fit, prediction, and handling of nonadditive patterns. The results support conclusions from recent studies (Dai & Busemeyer, 2014; Scholten et al., 2014), which suggest that attribute-wise mechanisms may be more suitable for describing intertemporal choices. Furthermore, the predictive performance was similar between the trade-off and the proportional difference (PD) models though the PD model is simpler.