Diffusion MRI (dMRI) enables non-invasive assessment of prostate microstructure but conventional dMRI metrics such as the Apparent Diffusion Coefficient in multiparametric MRI and reflect a mixture of underlying tissues features rather than distinct histologic characteristics. Integrating dMRI with the compartment-based biophysical VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumours) framework offers richer microstructural insights, though clinical gradient systems (40-80 mT/m) often suffer from poor signal-to-noise ratio at stronger diffusion weightings due to prolonged echo times. Ultra-strong gradients (e.g., 300 mT/m) can mitigate these limitations by improving SNR and contrast-to-noise ratios. This study investigates whether physics-informed self-supervised VERDICT (ssVERDICT) fitting when combined with ultra-strong gradient data, enhances prostate microstructural characterization relative to current fitting approaches and clinical gradient systems. We developed enhanced ssVERDICT fitting approaches using dense multilayer perceptron and convolutional U-Net architectures, comparing them against non-linear least-squares (NLLS) VERDICT fitting, original ssVERDICT implementation, and Diffusion Kurtosis Imaging across clinical- to ultra-strong gradient systems. For the same ultra-strong gradient data, Dense ssVERDICT outperformed NLLS VERDICT, boosting median CNR by 47%, cutting inter-patient Coefficient of Variation by 52%, and reducing pooled $f_{ic}$ variation by 50%. Overall, Dense ssVERDICT delivered the highest CNR, the most stable parameter estimates, and the clearest tumour-normal contrast compared with conventional fitting methods and clinical gradient systems. These findings underscore that meaningful gains in non-invasive prostate cancer characterization arise from the combination of advanced gradient systems and deep learning-based modelling.