In Paper I we presented the results of a study of the interrelationships between host galaxy magnitude, optical line luminosity, and radio luminosity in a large sample of Fanaroff-Riley classes 1 and 2 (FR 1 and FR 2) radio galaxies. We report several important differences between the FR 1 and FR 2 radio galaxies. At the same host galaxy magnitude or radio luminosity, the FR 2's produce substantially more optical line emission (by roughly an order of magnitude or more) than do FR 1's. Similarly, FR 2 sources produce orders of magnitude more line luminosity than do radio-quiet galaxies of the same optical magnitude, while FR 1 sources and radio-quiet galaxies of the same optical magnitude produce similar line luminosities. Combining these results with previous results from the literature, we conclude that while the emission-line gas in the FR 2's is indeed photoionized by a nuclear UV continuum source from the AGN, the emission-line gas in the FR 1's may be energized predominantly by processes associated with the host galaxy itself.The apparent lack of a strong UV continuum source from the central engine in FR 1 sources can be understood in two different ways. In the first scenario, FR l's are much more efficient at covering jet bulk kinetic energy into radio luminosity than FR 2's, such that an FR 1 has a much lower bolometric AGN luminosity (hence nuclear UV continuum source) than does an FR 2 of the same radio luminosity. We discuss the pros and cons of this model and conclude that the efficiency differences needed between FR 2 and FR 1 radio galaxies are quite large and may lead to difficulties with the interpretation since it would suggest that FR 2 radio source deposit very large amounts of kinetic energy into the ISM Intracluster Medium. However, this interpretation remains viable. Alternatively, it may be that the AGNs in FR 1 sources simply produce far less radiant UV energy than do those in FR 2 sources. That is, FR 1 sources may funnel a higher fraction of the total energy output from the AGNs into jet kinetic energy versus radiant energy than do FR 2 sources. If this interpretation is correct, then this suggests that there is a fundamental difference in the central engine and/or in the immediate "accretion region" around the engine in FR 1 and FR 2 radio galaxies. We note also the absence of FR 1 sources with nuclear broad line regions and suggest that the absence of the BLR is tied to the absence of the "isotropic" nuclear UV continuum source in FR 1 sources. We put forth the possibility that the FR 1/FR 2 dichotomy (i.e., the observed differences in the properties of low- and high-power radio sources) is due to qualitative differences in the structural properties of the central engines in these two types of sources. Following early work by Rees et al. (1982), we suggest the possibility that FR 1 sources are produced when the central engine is fed at a lower accretion rate, leading to the creation of a source in which the ratio of radiant to jet bulk kinetic energy is low, while FR 2 sources are produced when the central engine is fed at a higher accretion rate, causing the central engine to deposit a higher fraction of its energy in radiant energy. We further suggest the possibility that associated differences in the spin properties of the central black hole between FR 1 (lower spin) and FR 2 (higher spin) sources may be responsible for the different collimation properties and Mach numbers of the jets produced by these two types of radio-loud galaxies. This scenario, although currently clearly speculative, is nicely consistent with our current picture of the triggering, feeding, environments, and evolution of powerful radio galaxies. This model allows for evolution of these properties with time for example, the mass accretion rate and BH spin may decline with time causing an FR 2 radio source or quasar to evolve into a FR 1 radio source.