An analysis of observations of 50 radio-loud and radio-quiet quasars made by the X-ray satellite Ginga is presented. The spectra are the most accurate and sensitive yet obtained in the 2-20 keV band, and provide a unique opportunity to study the X-ray emission from these faint, although highly luminous, objects. The properties of the hard X-ray continuum are compatible with those of previous quasar surveys, with a highly significant variation of observed spectral indices which is unlikely to be due either to the radio heterogeneity of the sample or to spectral variability. The spectral variability shows no direct link to changes in luminosity. The spectra of the radio-quiet quasars are generally consistent with those of Seyfert galaxies, in support of current unification schemes, and there is also some evidence for the presence of Compton reflection and ionized absorption. However, a comparatively high percentage of quasars with soft spectra indicates that these features are unlikely to be present in all radio-quiet quasars. A comparison with recent ASCA observations of distant radio-quiet sources suggests that we may be seeing the start of a spectral transition between the low- luminosity Seyfert galaxies and these more powerful distant objects. It is shown for the first time that there is a definite range in the spectral index of radio-loud objects. Whether or not this is a direct indication of differing physical parameters in the nuclei of these objects is not known. It is possible that it is indirectly due to the observed relationship between radio core dominance and spectral index which has also been seen using the Einstein observatory. This relationship can be explained using a two-component beaming model, which also provides an explanation for the measured iron line strengths of the radio-loud objects.