We present a theoretical study of Cherenkov and transition radiation for swift electron beams penetrating dielectric nanospheres using material models of different sophistication. Specifically, we perform a combined time-domain (numerically, via the discontinuous Galerkin time-domain method) and frequency-domain (numerically and analytically, via Mie-based theory) study, including the induced-field distribution, cathodoluminescence (CL) multipole/directional decomposition, as well as the time-dependent angular power flow. For low velocities below the Cherenkov threshold, we show that transition radiation is dominant in the far-field CL, and the near-fields at the transition points are primarily responsible for the main features observed in the far-field. For higher velocities far beyond the Cherenkov threshold, we identify the fingerprints of the observable Cherenkov front. Specifically, a constant-permittivity model allows us to isolate the respective contributions of CR and TR to the far-field radiation, thereby facilitating the interpretation of the results for a more realistic material model that includes material resonances. Our combined time- and frequency-domain framework provides a direct view of radiative excitation channels for swift electron beams penetrating dielectric nanoparticles, thereby revealing their interplay beyond the conventional frequency-domain analyses.