The jet production efficiency of radio galaxies can be quantified by comparison of their kinetic jet powers $P_{jet}$ and Bondi accretion powers $P_B$. These two parameters are known to be related linearly, with the jet power resulting from the Bondi power by multiplication with an efficiency factor of order 1%. Using a recently published (Nemmen & Tchekhovskoy 2014) high-quality sample of 27 radio galaxies, I construct a $P_B$ - $P_{jet}$ diagram that includes information on optical AGN types as far as available. This diagram indicates that the jet production efficiency is a function of AGN type: Seyfert 2 galaxies seem to be systematically (with a false alarm probability of $4.3{ imes}10^{-4}$) less efficient, by about one order of magnitude, in powering jets than Seyfert 1 galaxies, LINERs, or the remaining radio galaxies. This suggests an evolutionary sequence from Sy 2s to Sy 1s and LINERs, controlled by an interplay of jets on the one hand and dust and gas in galactic nuclei on the other hand. When taking this effect into account, the $P_B$ - $P_{jet}$ relation is probably much tighter intrinsically than currently assumed.