Various structural, dynamic and thermodynamic properties of water molecules confined in single-wall carbon nanotubes (CNTs) are investigated using both polarizable and non-polarizable water models. The inclusion of polarizability quantitatively affects the nature of hydrogen bonding, which governs many properties of confined water molecules. Polarizable water leads to tighter hydrogen bonding and makes the distance between neighboring water molecules shorter than that for non-polarizable water. Stronger hydrogen bonding also decreases the rotational entropy and makes the diffusion constant smaller than in TIP3P and TIP3PM water models. The reorientational dynamics of the water molecules is governed by a jump mechanism, the barrier for the jump being highest for the polarizable water model. Our results highlight the role of polarizability in governing the dynamics of confined water and demonstrate that the inclusion of polarizability is necessary to obtain agreement with the results of ab initio simulations for the distributions of waiting and jump times. The SPC/E water model is found to predict various water properties in close agreement with the results of polarizable water models with much lower computational costs.