We describe microwave and hard X-ray observations of strong quasi-periodic pulsations from the GOES X1.3 solar flare on 2003 June 15. The radio observations were made jointly by the Owens Valley Solar Array (OVSA), the Nobeyama Polarimeter (NoRP), and the Nobeyama Radioheliograph (NoRH ). Hard X-ray observations were made by RHESSI. Using Fourier analysis, we study the frequency-and energy-dependent oscillation periods, differential phase, and modulation amplitudes of the radio and X-ray pulsations. Focusing on the more complete radio observations, we also examine the modulation of the degree of circular polarization and of the radio spectral index. The observed properties of the oscillations are compared with those derived from two simple models for the radio emission. In particular, we explicitly fit the observed modulation amplitude data to the two competing models. The first model considers the effects of MHD oscillations on the radio emission. The second model considers the quasiperiodic injection of fast electrons. We demonstrate that quasi-periodic acceleration and injection of fast electrons is the more likely cause of the quasi-periodic oscillations observed in the radio and hard X-ray emission, which has important implications for particle acceleration and transport in the flaring sources.