Substance dependent individuals (SDI) often exhibit decision-making deficits; however, it remains unclear whether the nature of the underlying decision-making processes is the same in users of different classes of drugs and whether these deficits persist after discontinuation of drug use. We used computational modeling to address these questions in a unique sample of relatively “pure” amphetamine-dependent (N = 38) and heroin-dependent individuals (N = 43) who were currently in protracted abstinence, and in 48 healthy controls (HC). A Bayesian model comparison technique, a simulation method, and parameter recovery tests were used to compare three cognitive models: (1) Prospect Valence Learning with decay reinforcement learning rule (PVL-DecayRI), (2) PVL with delta learning rule (PVL-Delta), and (3) Value-Plus-Perseverance (VPP) model based on Win-Stay-Lose-Switch (WSLS) strategy. The model comparison results indicated that the VPP model, a hybrid model of reinforcement learning (RL) and a heuristic strategy of perseverance had the best post-hoc model fit, but the two PVL models showed better simulation and parameter recovery performance. Computational modeling results suggested that overall all three groups relied more on RL than on a WSLS strategy. Heroin users displayed reduced loss aversion relative to HC across all three models, which suggests that their decision-making deficits are longstanding (or pre-existing) and may be driven by reduced sensitivity to loss. In contrast, amphetamine users showed comparable cognitive functions to HC with the VPP model, whereas the second best-fitting model with relatively good simulation performance (PVL-DecayRI) revealed increased reward sensitivity relative to HC. These results suggest that some decision-making deficits persist in protracted abstinence and may be mediated by different mechanisms in opiate and stimulant users.