We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H_2O and D_2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density rho (T), isothermal compressibility kappa _T(T), and self-diffusion coefficients D(T) of H_2O and D_2O are in excellent agreement with available experimental data; the isobaric heat capacity C_P(T) obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H_2O and D_2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H_2O and D_2O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H_2O, from PIMD simulations, is located at P_c = 167 pm 9 MPa, T_c = 159 pm 6 K, and rho _c = 1.02 pm 0.01 g/cm^3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D_2O is estimated to be P_c = 176 pm 4 MPa, T_c = 177 pm 2 K, and rho _c = 1.13 pm 0.01 g/cm^3. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, P_c = 203 pm 4 MPa, T_c = 175 pm 2 K, and rho _c = 1.03 pm 0.01 g/cm^3). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of T_c for D_2O and, particularly, H_2O suggest that improved water models are needed for the study of supercooled water.