To this end, we use NMR as a prominent showcase and introduce an extensive EFG database for the commercial, high-performance Li-ion battery material Li 4 Ti 5 O 12 (LTO). LTO is particularly suitable for such benchmark purposes as all three of its constituent species are quadrupolar and because its ionic mobility has been repeatedly studied by advanced Li NMR experiments. We correspondingly assemble a database of 68,880 EFG tensors calculated for all three atomic species and for a wide range of interatomic distances that reflect those probed in the measurements. We then derive a performance metric for key NMR observables that is used in the optimization and assessment of scalar and tensor EFG ML models. This indeed reveals an order of magnitude superiority in predictive performance for an explicit learning of the full EFG tensor. The failure of the symmetry-agnostic scalar approach is instead traced back to its inability of capturing especially the orientation of the EFG tensor, which the experimental observables sensitively depend on.