Slip lengths reported from molecular dynamics (MD) simulations of water flow in graphene nanochannels show significant scatter in the literature. These discrepancies are in part due to the used water models. We demonstrate self-consistent comparisons of slip characteristics between the SPC, SPC/E, SPC/Fw, TIP3P, TIP4P, and TIP4P/2005 water models. The slip lengths are inferred using an analytical model that employs the shear viscosity of water and channel average velocities obtained from nonequilibrium MD simulations. First, viscosities for each water model are quantified using MD simulations of counterflowing, force-driven flows in periodic domains in the absence of physical walls. While the TIP4P/2005 model predicts water viscosity at the specified thermodynamic state with 1.7% error, the predictions of SPC/Fw and SPC/E models exhibit 13.9% and 23.1% deviations, respectively. Water viscosities obtained from SPC, TIP4P, and TIP3P models show larger deviations. Next, force-driven water flows in rigid (cold) and thermally vibrating (thermal) graphene nanochannels are simulated, resulting in pluglike velocity profiles. Large differences in the flow velocities are observed depending on the used water model and to a lesser extent on the choice of rigid vs thermal walls. Depending on the water model, the slip length of water on cold graphene walls varied between 34.2 nm and 62.9 nm, while the slip lengths of water on thermal graphene walls varied in the range of 38.1 nm-84.3 nm.