Important goals of BNL RHIC and CERN LHC experiments with ion beams include the creation and study of new forms of matter, such as the quark gluon plasma. Heavy quark production and attenuation provide unique tomographic probes of that matter. We predict the suppression pattern of open charm and beauty in Au+Au collisions at RHIC and LHC energies based on the DGLV formalism of radiative energy loss. A cancellation between effects due to the sqrt[s] energy dependence of the high p(T) slope and heavy quark energy loss is predicted to lead to surprising similarity of heavy quark suppression at RHIC and LHC.