We present the first-principles molecular dynamics simulations of water molecules using two different levels of density functional theory within the Kohn-Sham scheme, namely, Becke-Lee-Yang-Parr (BLYP) and Perdew-Burke-Ernzerhof (PBE) with dispersion corrections such as D2 as well as D3 versions of Grimme dispersion correction and dispersion-corrected atom-centered potential. Our aim is to provide a comparative study of these functionals in explaining the thermophysical and structural properties along with nondiffusive jump dynamics of water molecules concerning the experimental data. The hydrogen bonding phenomenon is dependent on polarity, bonding, as well as nonbonding interactions, which requires thorough parametrization. Since hydrogen bonding is responsible for several properties in the water, we investigate the effect of dispersion corrections on the hydrogen bond jump dynamics. BLYP and PBE functionals are well-known for overestimating the spatial structure and underestimating the density and diffusivity. Thus, dispersion corrections are introduced to generate a well-structured and adequately dense equilibrated liquid water system. Here, we have reported the density values of water obtained from different density functionals and also verified the trend with other thermophysical phenomena such as compressibility and cohesive energy. The behavior of simulated water systems is further explained by analyzing various structural properties and hydrogen bond jump dynamics.