The energy correlations are among the best studied observables both experimentally and theoretically. Recent studies revealed that the energy correlations in multi-particle final states exhibit two characteristic regimes as functions of the angular separations between the calorimeters: power-like growth at small angles and slowly varying function at larger angles. We argue that the transition between the two regimes is controlled by the scaling dimension of the heavy operators and the dynamics of the theory. We analyze this phenomenon in detail in the planar N = 4 SYM theory both at weak and strong coupling. An analogous transition was previously observed in QCD in the measurement of the angular energy distribution of particles belonging to the same energetic jet. In that case it corresponds to the transition from the perturbative regime described in terms of correlations between quarks and gluons to the non-perturbative regime described in terms of correlations between hadrons.