The particle size distribution (PSD) in emulsion polymerization (EP) has been modeled in the past using either the pseudo bulk (PB) or the 0-1/0-1-2 approaches. There is some controversy on the proper type of model to be used to simulate the experimental PSDs, which are apparently broader than the theoretical ones. Additionally, the numerical technique employed to solve the model equations, involving hyperbolic partial differential equations (PDEs) with moving and possibly steep fronts, has to be precise and robust, which is not a trivial matter. A deterministic kinetic model for the PSD evolution of ab initio EP of vinyl monomers was developed to investigate these issues. The model considers three phases, micellar nucleation, and particles that can contain $n\ge 0$ radicals. Finite volume (FV) and weighted-residual methods are used to solve the system of PDEs and compared; their limitations are also identified. The model was validated by comparing predictions with data of monomer conversion and PSD for the batch emulsion homopolymerization of styrene (Sty) and methyl methacrylate (MMA) using sodium dodecyl sulfate (SDS)/potassium persulfate (KPS) at 60 °C, as well as the copolymerization of Sty-MMA (50/50; mol/mol) at 50 and 60 °C. It is concluded that the PB model has a structural problem when attempting to adequately represent PSDs with steep fronts, so its use is discouraged. On the other hand, there is no generalized evidence of the need to add a stochastic term to enhance the PSD prediction of EP deterministic models.