Conventional magnetic resonance imaging (cMRI) in multiple sclerosis (MS) patients provides measures of focal brain damage and activity, which are fundamental for disease diagnosis, prognosis, and the evaluation of response to therapy. However, cMRI is insensitive to the damage to the microenvironment of the brain tissue and the heterogeneity of MS lesions. In contrast, the damaged tissue can be characterized by mathematical models on multishell diffusion imaging data, which measure different compartmental water diffusion. In this work, we obtained 12 diffusion measures from eight diffusion models, and we applied a deep-learning attention-based convolutional neural network (CNN) (GAMER-MRI) to select the most discriminating measures in the classification of MS lesions and the perilesional tissue by attention weights. Furthermore, we provided clinical and biological validation of the chosen metrics-and of their most discriminative combinations-by correlating their respective mean values in MS patients with the corresponding Expanded Disability Status Scale (EDSS) and the serum level of neurofilament light chain (sNfL), which are measures of disability and neuroaxonal damage. Our results show that the neurite density index from neurite orientation and dispersion density imaging (NODDI), the measures of the intra-axonal and isotropic compartments from microstructural Bayesian approach, and the measure of the intra-axonal compartment from the spherical mean technique NODDI were the most discriminating (respective attention weights were 0.12, 0.12, 0.15, and 0.13). In addition, the combination of the neurite density index from NODDI and the measures for the intra-axonal and isotropic compartments from the microstructural Bayesian approach exhibited a stronger correlation with EDSS and sNfL than the individual measures. This work demonstrates that the proposed method might be useful to select the microstructural measures that are most discriminative of focal tissue damage and that may also be combined to a unique contrast to achieve stronger correlations to clinical disability and neuroaxonal damage.