We present a comprehensive study of the relation between radio and X-ray emission in neutron star (NS) X-ray binaries, use this to infer the general properties of the disc-jet coupling in such systems and compare the results quantitatively with those already established for black hole (BH) systems. There are clear qualitative similarities between the two classes of object: hard states below about 1 per cent of the Eddington luminosity produce steady jets, while transient jets are associated with outbursting and variable sources at the highest luminosities. However, there are important quantitative differences: the NSs are less radio loud for a given X-ray luminosity (regardless of mass corrections) and they do not appear to show the strong suppression of radio emission in steady soft states that we observe in BH systems. Furthermore, in the hard states, the correlation between radio and X-ray luminosities of the NS systems is steeper than the relation observed in BHs by about a factor of 2. This result strongly suggests that the X-ray emission in the BH systems is radiatively inefficient, with an approximate relation of the form Graphic, consistent with both advection-dominated models and the jet-dominated scenario. In contrast, the jet power in both classes of object scales linearly with accretion rate. This constitutes some of the first observational evidence for the radiatively inefficient scaling of X-ray luminosity with accretion rate in accreting BH systems. Moreover, based on simultaneous radio/X-ray observations of Z-type NSs (the brightest of our Galaxy, always near or at the Eddington accretion rate), we draw a model that can describe the disc-jet coupling in such sources, finding a possible association between a particular X-ray state transition [horizontal branch to normal branch] and the emission of transient jets.