Staggered and Co-located grids are the two conventional grid systems utilized in Computational Multi-Fluid Dynamics (CMFD). Even though difficult to implement, staggered grid has been a popular choice over co-located in CMFD for more than two decades as compared to CFD on a co-located grid. In this study, these issues are addressed with our in-house level set method-based codes on staggered and co-located grid with diffuse and sharp interface approach. These developments lead us to the conclusion that momentum interpolation method (MIM) and balanced force method (BFM) are essential for diffuse interface approach on co-located grid, while only MIM is essential for sharp interface approach on co-located grid. The performances of these methodologies (DI-LSM_stag, DI-LSM_col, SI-LSM_stag and SI-LSM_col) are compared on a dam break and falling droplet problems. The validation/verification of these methodologies shows excellent agreement with published results. Performance study with these problems reveals that, for gravity dominant problem (dam break), the diffuse interface approach (especially staggered) is taking lesser time than sharp interface approach (staggered and co-located). Whereas for the surface tension dominant falling droplet problem, the sharp interface approach (staggered and co-located) takes lesser time as compared to diffuse interface approach (staggered and co-located).