Deep learning rainfall-runoff models have shown the ability to reproduce the observed hydrograph exceeding the performance of physics-based models, but their reliability outside the training distribution is still an open question. Most robustness evaluation have focused on a single architecture (LSTM), and have used controlled forcing perturbations (temperature offset or precipitation scaling) to probe the non-stationarity condition. In this study, we evaluate the robustness of five deep learning architectures (LSTM, minLSTM, minGRU, MLP-Mixer, Transformer) against a re-calibrated physics-based benchmark (SAC-SMA + Snow-17) across 554 CAMELS catchments, driven by a six-Global Change Model (GCM), four-Shared Socioeconomic Pathway (SSP) NEX-GDDP-CMIP6 and three-future periods ensemble. The results show that the deep learning models outperform the physics-based benchmark in terms of accuracy, but their robustness is limited under non-stationary conditions. The LSTM and minGRU architectures show the best performance among the deep learning models, while the MLP-Mixer and minLSTM architectures show the worst performance. We found that the predictive skill does not imply robustness: the LSTM, the most accurate architecture, is the least robust. Transformer, the most robust on annual volumes, fails to reproduce the intra-annual redistribution of streamflow, diverging from the physics-based benchmark in both directions, compensating that difference at annual basis. Architecture, not GCMs, SSPs nor period, is the dominant factor of divergence (45 % of the evaluated catchments). The results highlight the need for a more comprehensive evaluation of deep learning models under non-stationary conditions, and the importance of considering both accuracy and robustness in model selection.