AGNs and GRBs produce powerful relativistic jets and their central engines share the same basic astrophysical ingredients, despite the vastly different mass scales. An outstanding question is how the jet physics scales from GRBs up to AGNs. Using Fermi and Swift observations, we find evidence that the jets produced by blazars and long-duration GRBs follow the same correlation between the intrinsic gamma-ray luminosity and kinetic power. This result suggests that jet production and energy dissipation mechanisms are remarkably similar over 10 orders of magnitude in jet power, establishing a physical analogy between AGN and GRBs. We will discuss the implications of these results in terms of the properties of the central engines of AGNs and GRBs such as the radiative efficiency, bulk Lorentz factor and jet opening angles.