In this research, we propose a comprehensive study aimed at advancing the understanding and applicability of several models for the capturing of the fluid interface in Direct Numerical Simulations (DNS) of multiphase flows. The primary objective is to analyze and contrast the performance of sharp and diffuse interface approaches. To this end, a series of numerical simulations is conducted by using an in-house solver with different interface capturing methods. These simulations aim to reproduce commonly used benchmark test cases and more complex practical applications, such as the sloshing phenomena of fluids within containers. Specifically, we compare the properties of algebraic TVD [1] and geometric PLIC [2] Volume of Fluid (VOF) methods, which employ a sharp interface description, with two phase field models, based respectively on the profile-corrected Cahn-Hilliard [3] and conservative Allen-Cahn formulations [4], where diffuse interfaces are employed instead. The study reveals the strengths and weaknesses of each method under different conditions, shedding light on their accuracy. The outcomes provide valuable insights for researchers in selecting the most suitable numerical model for their specific applications.