We use published data on the power and production efficiency of jets in blazars with double radio lobes in order to compare results obtained using different methods. In order to eliminate selection effects, we use cross-matched sub-samples containing only luminous blazars. We compare the three main existing methods, namely those based on the emission of radio lobes, on spectral fitting, and on radio core shift. We find the average jet power obtained for identical samples with the radio-lobe method is ∼10 times lower than that from the spectral fitting. In turn, the power from spectral fitting is compatible with that from core-shift modelling for plausible parameters of the latter. We also consider a phenomenological estimator based on the γ-ray luminosity. We examine uncertainties of those methods and discuss two alternative hypotheses. In one, the blazar-fit and core-shift methods are assumed to be correct, and the lower power from radio lobes is caused by intermittency of accretion. Long periods of quiescence cause the energy in the radio lobes, accumulated over the lifetime of the blazar, to be much less than that estimated based on the present luminous state. In addition, the power calculated using the radio lobes can be underestimated for intrinsically compact jets, in which the radio core flux can be over-subtracted. In our second hypothesis, the radio-lobe method is assumed to be correct, and the blazar-fit and core-shift powers are reduced due to the presence of ∼15 pairs per proton and a larger magnetization than usually assumed, respectively.