Chemically complex multicomponent alloys have garnered widespread interest owing to their exceptional properties coming from a sheer inexhaustible compositional space. The complexity poses severe challenges for atomistic modelling and interatomic potential development. Here, we explore the limits of two complementary state-of-the-art machine-learned potentials—the moment tensor potential (MTP) and the Gaussian moment neural network (GM-NN)—in simultaneously describing both the configurational and vibrational degrees of freedom in the prototype Ta-V-Cr-W alloy family. Both models are equally accurate with exceptional performance in comparison to classical potentials. A single potential is able to achieve root-mean-square-errors of 1.37-4.35 meV/atom and 0.023-0.057 eV/Å in 0 K energies and forces, respectively, across all subsystems of the alloy family, and 0.156-0.179 eV/Å in high-temperature molecular dynamics forces for the disordered quaternary. MTPs achieve faster convergence with the training size than the GM-NNs, whereas GM-NNs are faster in execution. Active learning is partially beneficial and has to be complemented with a conventional human-based training set generation.