Neural-network-based constitutive models are increasingly recognized as a powerful approach for autonomous, data-driven material modeling in computational mechanics. However, a fundamental question remains inadequately addressed: What level of training data complexity is necessary to ensure robust and reliable material model performance? In this work, we address this question by systematically contrasting two distinct experimental data regimes: (i) advanced full-field measurements acquired via digital image correlation (DIC), and (ii) homogeneous stress–strain datasets derived from biaxial tension experiments. Leveraging a unified constitutive artificial neural network (CANN) framework, we train separate models on each data regime and rigorously evaluate their numerical robustness, stability, and predictive accuracy. A central component of our analysis is a comprehensive investigation of regularization requirements. We systematically examine which regularization techniques are optimal for each training regime, quantify their necessary enforcement, and elucidate their effects on convergence, stability, and generalization. These regularization strategies are explicitly embedded within our evaluation protocol. To assess generalizability, we conduct bidirectional cross-evaluation: models trained on homogeneous data are tested against full-field responses, while models trained on full-field data are evaluated on homogeneous benchmark behaviors. This comparative study elucidates the practical trade-offs among data richness, regularization demands, and model robustness, offering concrete guidelines on when conventional datasets suffice and when full-field measurements are essential.