Observed and simulated galaxies exhibit a significant variation in their velocity dispersion profiles. We examine the inner and outer slopes of stellar velocity dispersion profiles using integral field spectroscopy data from two surveys, SAMI (for z < 0.115) and CALIFA (for z < 0.03), comparing them with results from two cosmological hydrodynamic simulations: Horizon-AGN (for z = 0.017) and NewHorizon (for z ≲ 1). The simulated galaxies closely reproduce the variety of velocity dispersion slopes and stellar mass dependence of both inner and outer radii (0.5 r ₅₀ and 3 r ₅₀) as observed, where r ₅₀ stands for half-light radius. The inner slopes are mainly influenced by the relative radial distribution of the young and old stars formed in situ: a younger center shows a flatter inner profile. The presence of accreted (ex situ) stars has two effects on the velocity dispersion profiles. First, because they are more dispersed in spatial and velocity distributions compared to in situ formed stars, it increases the outer slope of the velocity dispersion profile. It also causes the velocity anisotropy to be more radial. More massive galaxies have a higher fraction of stars formed ex situ and hence show a higher slope in outer velocity dispersion profile and a higher degree of radial anisotropy. The diversity in the outer velocity dispersion profiles reflects the diverse assembly histories among galaxies.