Understanding the underlying mechanism to growth of a material greatly assists control over its synthesis. In this investigation, we employ density functional theory to calculate the desorption and diffusion energy barriers to growth of MoS$_2$ and WS$_2$ from a M-C-O-H-S system on c-plane alpha sapphire, a commonly used substrate. We then perform experiments and use these numbers within a nucleation theory framework to explain growth characteristics. Nucleation rates, densities, and step velocities are predicted and analyzed. In particular, differences between MoS$_2$ and WS$_2$ growth-larger nucleation densities and small island sizes in WS$_2$ compared to MoS$_2$-are explained and correlated to the differences between energy barriers to desorption and diffusion of W and Mo.