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The power-law energy distribution observed in dissipation events ranging from flares down to nanoflares has been associated either to intermittent turbulence or to self-organized criticality. Despite the many studies conducted in recent years, it is unclear whether these two paradigms are mutually exclusive or they are complementary manifestations of the complexity of the system. We numerically integrate the magnetohydrodynamic equations to simulate the dynamics of coronal loops driven at their bases by footpoint motions. After a few photospheric turnover times, a stationary turbulent regime is reached, displaying a broadband power spectrum and a dissipation rate consistent with the cooling rates of the plasma confined in these loops. Our main goal is to determine whether the intermittent features observed in this turbulent flow can also be regarded as manifestations of self-organized criticality. A statistical analysis of the energy, area, and lifetime of the dissipative structures observed in these simulations displays robust scaling laws. We calculated the critical exponents characterizing the avalanche dynamics, and the spreading exponents that quantify the growth of these structures over time. In this work we also calculate the remaining critical exponents for several activity thresholds and verify that they satisfy the conservation relations predicted for self-organized critical systems. These results can therefore be regarded as a bona fide test supporting that the stationary turbulent regimes characterizing coronal loops also correspond to states of self-organized criticality. [ABSTRACT FROM AUTHOR]