To gain new insights into the radio-loud/radio-quiet dichotomy reported for active galactic nuclei (AGN), we examine radio loudness as a function of Eddington ratio for a previously published sample of 199 AGN from five different populations. After initially considering radio loudnesses derived using total radio luminosities, we repeat the investigation using core radio luminosities only, applying a previously established mass correction for these core luminosities. In both cases, for Eddington ratios <1 per cent, Fanaroff–Riley type I and broad-line radio galaxies are on average more radio-loud than Seyfert and low-ionization nuclear emission-line region galaxies. However, the distribution of radio loudnesses for the mass-corrected, core-only sample is much narrower than that of the clearly bimodal total radio loudness distribution. The advantages and disadvantages of using core- or lobe-dominated radio luminosity as a measure of instantaneous jet power are discussed. We furthermore compare the core and total radio luminosities for the entire sample, as well as illustrating the importance of the mass term by comparing the AGN with a sample of black hole X-ray binaries. We conclude that if the mass-corrected core radio luminosity is a good measure of jet power, then black hole spin may have considerably less impact on jet power than previously reported, or that our sample does not include the extremes of spin. If the spread in jet power is small, then we suggest that characteristics of the ambient environment and/or the radio source age could be equally as important in producing a radio-loudyradio-quiet dichotomy seen in total radio luminosity.