This paper proposes a comparison between an Assisted Synchronous Reluctance Machine (SyRMA) and a non-assisted synchronous machine for which a Dual Phase (DP) material is used in the rotor's structure (SyRMDP). Both types of machines, that must operate at high speeds, are designed thanks to the same optimization approach. However, the SyRMA model includes an analytic model which takes into account the mechanical stress on the magnetic bridges due to the centrifugal force in high speed operations. The performance of these two optimally designed machines are compared for applications up to 15000 rpm.