By comparing a kinetic and a thermal-equilibrium theory of polariton Bose-Einstein condensation, we study under what conditions the dynamical condensation under steady-state non-resonant pumping can approach thermal equilibrium. In particular, we study the dependence on two material parameters: the vacuum-field Rabi-splitting and the polariton radiative lifetime. When increasing the Rabi splitting, condensation takes place under strong non-equilibrium conditions, with dominating quantum fluctuations. Increasing the polariton lifetime above 10 ps at moderate Rabi splitting, instead, produces a quasi-equilibrium condensate at low exciton density, consistently with the picture of a weakly interacting Bose gas. (C) 2007 Elsevier Ltd. All rights reserved.