Development of experimental techniques for characterization of magnetic properties at high spatial resolution is essential for progress in miniaturization of magnetic devices, for example, in data storage media. Inelastic scattering of electron vortex beams (EVBs) was recently reported to contain atom-specific magnetic information. We develop a theoretical description of inelastic scattering of EVBs on crystals and perform simulations for EVBs of different diameters. We show that use of an EVB wider than an interatomic distance does not provide any advantage over an ordinary convergent beam without angular momentum. On the other hand, in the atomic-resolution limit, electron energy loss spectra measured by EVBs are strongly sensitive to the spin and orbital magnetic moments of studied matter, when channeling through or very close to the atomic columns. Our results demonstrate the boundaries for efficient use of EVBs in measurement of magnetic properties.