In this paper, we study the primary atomization characteristics of liquid jet injected into a gaseous crossow through direct numerical simulations (DNS) and large eddy simulations (LES). The DNS use a coupled level set volume of uid (CLSVOF) sharp interface capturing method resolving all relevant scales to predict the drop size distribution (DSD) for drops larger than the grid spacing. The LES use a volume of uid (VOF) diused interface method modelling the sub grid droplets. The purpose of this paper is to provide a comparison of the results of drop data between DNS and LES. The simulations are performed for a liquid jet injection with liquid-gas momentum ux ratio of 6.6, liquid jet Reynolds number of 14,000 injected into a crossowing air with Reynolds number 570,000 and Weber number of 330 at a liquid-togas density ratio of 10. Two distinct and simultaneous atomization/breakup mechanisms have been observed in the simulations: column/bag breakup and ligament/surface breakup. It was found that the DSDs obtained from the DNS and LES each follow a log-normal distribution based on their respective droplet diameter data. An overlap region exists between the individual DSDs from the DNS and LES when combined. The width of this overlap region decreases along the downstream direction. A log-normal distribution is found to be a good t to the combined DSD incorporating both resolved and sub-grid droplets. This information is relevant for the secondary atomization simulations and modeling.