A sample of 18 286 radio-loud active galactic nuclei (AGN) is presented, constructed by combining the seventh data release of the Sloan Digital Sky Survey with the NRAO (National Radio Astronomy Observatory) VLA (Very Large Array) Sky Survey (NVSS) and the Faint Images of the Radio Sky at Twenty centimetres (FIRST) survey. Using this sample, the differences between radio galaxies of ‘high-excitation’ (‘quasar-mode’; hereafer HERG) and ‘low-excitation’ (‘radio-mode’; LERG) are investigated. A primary difference between the two radio source classes is the distinct nature of the Eddington-scaled accretion rate on to their central black holes: HERGs typically have accretion rates between one per cent and 10 per cent of their Eddington rate, whereas LERGs predominately accrete at a rate below one per cent Eddington. This is consistent with models whereby the population dichotomy is caused by a switch between radiatively efficient and radiatively inefficient accretion modes at low accretion rates. Local radio luminosity functions are derived separately for the two populations, for the first time, showing that although LERGs dominate at low radio luminosity and HERGs begin to take over at L1.4 GHz∼ 1026 W Hz−1, examples of both classes are found at all radio luminosities. Using the V/Vmax test it is shown that the two populations show differential cosmic evolution at fixed radio luminosity: HERGs evolve strongly at all radio luminosities, while LERGs show weak or no evolution. This suggests that the luminosity dependence of the evolution previously seen in the radio luminosity function is driven, at least in part, by the changing relative contributions of these two populations with luminosity. The host galaxies of the radio sources are also distinct: HERGs are typically of lower stellar mass, with lower black hole masses, bluer colours, lower concentration indices and less pronounced 4000 Å breaks indicating younger stellar populations. Even if samples are matched in radio luminosity and stellar and black hole masses, significant differences still remain between the accretion rates, stellar populations and structural properties of the host galaxies of the two radio source classes. These results offer strong support to the developing picture of radio-loud AGN in which HERGs are fuelled at high rates through radiatively efficient standard accretion discs by cold gas, perhaps brought in through mergers and interactions, while LERGs are fuelled via radiatively inefficient flows at low accretion rates. In this picture, the gas supplying the LERGs is frequently associated with the hot X-ray haloes surrounding massive galaxies, groups and clusters, as part of a radio-AGN feedback loop.