Structural, thermodynamic, and dielectric properties of three polarizable and two nonpolarizable water models are compared with experimental data at four different thermodynamic states from ambient to supercritical conditions. Pair-correlation functions and thermodynamic data are obtained from Monte Carlo simulations, performed both on the (N,V,T) and (N,p,T) ensembles. The dielectric constants are determined with the molecular Ornstein-Zernike theory. It is found that the polarizable models can reproduce the experimental structure considerably better than the nonpolarizable ones at the high-temperature states. In particular, the elongation of the hydrogen bonds with increasing temperature, which is observed by neutron diffraction measurements, in only seen in the simulations with the polarizable potential models. On the other hand, the polarizable models fail to describe the correct temperature dependence of the thermodynamic properties. Although at ambient conditions they overestimate both the density and the dielectric constant of the system, around the critical temperature they result in 10%-50% lower densities than the experimental values. The obtained magnitude of the internal energies as well as the dielectric constants are also considerably smaller than their experimental values at these thermodynamic state points. The results of this study point out the need of new polarizable water models which, besides the reasonable reproduction of the experimental pair-correlation functions, are also able to describe the dependence of the thermodynamic properties on the temperature and pressure.