In a comparative study of the dissipative behavior of various classes of high-Tc superconductors in large magnetic fields, we demonstrate that materials with a large electronic anisotropy, like the Bi and Tl compounds, have intrinsically smaller pinning energies than more isotropic materials. Consequently, the highly anisotropic materials exhibit thermally assisted dissipation down to temperatures far below Tc. In spite of small pinning energies, large critical current densities Jc can be observed in the critical-state regime at T<Tcr. In this regime irradiation damage produces large changes in Jc, but only modest changes in the magnitude of the pinning energies as evidenced in the thermally activated regime. We introduce a general criterion, which denotes the temperature and magnetic-field regime in which superconductors can be applied.