Model-based cognitive neuroscience links cognitive models to functional brain recordings to uncover the neural mechanisms underlying decision-making. However, it remains unclear which model best yields reliable inferences from empirical data, particularly when EEG signals are contaminated by noise. This study compares two single-trial joint models, the directed and integrative models, using drift-diffusion modeling (DDM) and EEG data. The directed model posits that EEG measures influence cognitive parameters, whereas the integrative model assumes both behavioral and neural signals reflect shared latent processes. We simulate decision-making data with varying EEG signal-to-noise ratios (SNRs) and EEG-behavior coupling strengths to assess how well each model recovers the true latent cognitive parameters. We hypothesize that the directed model will perform better under high-SNR and weak-coupling conditions, while the integrative model will excel under low-SNR and strong-coupling conditions. This simulation-based approach highlights each model’s strengths and limitations for real-world applications, particularly in addressing noise-contaminated EEG recordings.