We have examined the angular distributions of medium-energy (500--1500 eV) elastically backscattered electrons from bulk Cu(001) and Ni(001) crystals and from pseudomorphic Cu on Ni(001). The observed diffraction features are largely governed by forward scattering of the outgoing electrons, and incoming beam scattering appears to play a relatively minor role. This conclusion is reached by comparing these angular distributions with theoretical angular distributions, and with those obtained via angle-resolved Auger electron and x-ray photoelectron diffraction spectroscopies involving electrons of comparable kinetic energies. We find that the three experimental techniques yield very similar results, indicating that incident beam effects and the mode of excitation play a minor role. In the calculations, we have both included and neglected incident beam diffraction. By including incoming beam diffraction, we have for simplicity ignored the phase relationship between incoming and outgoing beams. The result is that inclusion of incoming beam scattering does not particularly improve the level of agreement between theory and experiment relative to calculations which neglect incoming beam diffraction. Moreover, the level of agreement between experiment and theory is quite good for the simpler theory which only treats outgoing electron scattering. Finally, we find that azimuthal-angle medium-energy backscattered electron diffraction scans for pseudomorphic Cu/Ni(001) are not as sensitive to elastic overlayer strain as are polar-angle scans. The latter measurement provides a highly sensitive method of measuring strain which is quite straightforward to interpret.