In a previous paper we presented a homogeneous and 92% complete optical spectral dataset of the 3CR radio sources with redshift <0.3. Here we use the emission line measurements to explore the spectroscopic properties of the sample. The 3CR sources show a bimodal distribution of excitation index, a new spectroscopic indicator that measures the relative intensity of low and high excitation lines. This unveils the presence of two main sub-populations of radio-loud AGN to which we refer to, following previous studies, as high and low excitation galaxies (HEG and LEG, respectively). In addition to the two main classes, we find one source with a spectrum typical of star forming galaxies, and 3 objects of extremely low level of excitation. All broad-line objects are HEG from the point of view of their narrow emission line ratios and all HEG are FR II radio-galaxies with log L 178 [erg s −1 ] > ∼ 32.8. Conversely LEG cover the whole range of radio power encompassed by this 3CR subsample (30.7 < ∼ log L 178 < ∼ 35.4) and they are of both FR I and FR II type. The brightest LEG are all FR II. HEG and LEG obey to two (quasi) linear correlations between the optical line and extended radio luminosities, with HEG being brighter than LEG in the [O III] line by a factor of ∼10. HEG and LEG are offset also in a plane that compares the black hole mass and the ionizing nuclear luminosity. However, although HEG are associated with higher nuclear luminosities, we find LEG among the brightest radio sources of the sample and with a clear FR II morphology, indistinguishable from those seen in HEG. This suggests that LEG are not simply objects with a lower level of accretion. We speculate that the differences between LEG and HEG are related to a different mode of accretion: LEG are powered by hot gas, while HEG require the presence of cold accreting material. The high temperature of the accreting gas in LEG accounts for the lack of "cold" structures (i.e. molecular torus and broad line region), for the reduced radiative output of the accretion disk, and for the lower gas excitation.