The relative contributions of in-plane (damping-like) and out-of-plane (field-like) spin-transfer torques (STT) in the magnetization switching of out-of-plane magnetized magnetic tunnel junctions (pMTJ) has been theoretically analyzed using the transformed Landau-Lifshitz-Gilbert (LLG) equation with the STT terms. It is demonstrated that in a pMTJ structure obeying macrospin dynamics, the out-of-plane torque influences the precession frequency, but it does not contribute significantly to the STT switching process (in particular to the switching time and switching current density), which is mostly determined by the in-plane STT contribution. This conclusion is confirmed by finite temperature and finite writing pulse macrospin simulations of the current field switching diagrams. It contrasts with the case of STT switching in in-plane magnetized magnetic tunnel junction (MTJ) in which the field-like term also influences the switching critical current. This theoretical analysis was successfully applied to the interpretation of voltage field STT switching diagrams experimentally measured on pMTJ pillars 36 nm in diameter, which exhibit macrospin behavior. The physical nonequivalence of Landau and Gilbert dissipation terms in the presence of STT-induced dynamics is also discussed.