Background and Purpose: Prompt gamma-ray timing (PGT) and prompt gamma-ray spectroscopy (PGS) are non-invasive techniques for dose delivery monitoring in proton radiotherapy. Integrating PGT and PGS into a unified data analysis framework may improve proton range verification by incorporating both temporal and spectral information from prompt gamma-ray events. This study evaluates the effectiveness of this integration for enhancing the accuracy of proton range verification using machine-learning. Material and Methods: A homogeneous phantom was irradiated with 162 and 225 MeV static and scanned proton beams. Air cavities of 5, 10 and 20 mm were introduced to simulate anatomical variations. The energy and time of arrival of prompt gamma rays were measured using a PGT detector. 2-dimensional time-energy spectra were extracted for 1,440 proton spots. Different feature sets (energy-only, time-only, energy-restricted time, image) were computed. These feature sets were used by four different machine-learning models to predict range shifts. Model performance was assessed using the root mean square error (RMSE). Results: Time-only and combined time-energy feature sets exhibited good performance with RMSE values of 3 to 4 mm, consistent with previously developed models. Energy-only and image features led to poorer performance with RMSE values exceeding 5 mm. The integration of energy-only features did not improve prediction accuracy compared to exclusively using time-only features. Conclusion: While spectral information did not contribute additional value for determining proton beam range shifts in the investigated setup, the findings show that temporal information alone is sufficient to perform accurate proton range verification.