A leading explanation for the origin of Galactic cosmic rays is acceleration at strong shock waves in the collisionless plasma surrounding young supernova remnants. Evidence for this is provided by multiwavelength non-thermal emission thought to be associated with ultrarelativistic electrons at these shocks. However, the dependence of the electron acceleration process on the orientation of the upstream magnetic field with respect to the local normal to the shock front (quasi-parallel/quasi-perpendicular), as well as on the shock Mach number, is still being debated. Data taken by the Cassini spacecraft at Saturns bow shock has revealed many examples of electron acceleration under quasi-perpendicular conditions, but also the first example of electron acceleration at a quasi-parallel shock up to at least MeV energies. Here we present those data surveyed in a systematic way, and make in particular the first detailed comparison between the electron energy spectra resulting in differing upstream magnetic field regimes. We discuss whether the acceleration is consistent with diffusive shock acceleration theory in each case, and comment on a role of energy-dependent interaction between the electrons and short, large-amplitude magnetic structures present in the upstream of high-Mach number quasi-parallel shocks.