  The evolution of powerful extragalactic jets is not only interesting by
itself, but also for its impact on the evolution of the host galaxy and its
surroundings. We have performed long-term axisymmetric numerical simulations of
relativistic jets with different powers to study their evolution through an
environment with a pressure and density gradient. Our results show key
differences in the evolution of jets with different powers in terms of the
spatial and temporal scales of energy deposition. According to our results, the
observed morphology in X-ray cavities requires that an important fraction of
the jet's energetic budget is in the form of internal energy. Thus, light,
lepton-dominated jets are favoured. In all cases, heating is mainly produced by
shocks. Cavity overpressure is sustained by an important population of thermal
particles. Our simulations reproduce the cool-core structure in projected,
luminosity-weighted temperature. We have performed an additional simulation of
a slow, massive jet and discuss the differences with its relativistic
counterparts. Important qualitative and quantitative differences are found
between the non-relativistic and the relativistic jets. Our conclusions point
towards a dual-mode of AGN kinetic feedback, depending on the jet power.
