The radiative and collisional parton energy losses in an expanding quark-gluon plasma are compared. The radiative energy loss is calculated within the light-cone path integral approach . The collisional energy loss is calculated using the Bjorken method with an accurate treatment of the binary collision kinematics. Our numerical results demonstrate that, for RHIC and LHC conditions, the collisional energy loss is relatively small in comparison with the radiative. An enhancement of the heavy quark radiative energy loss is found as compared to that of light quarks at high energies.