Numerical techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau and least-squares, are evaluated for the solution of transient population balance (PB) models describing liquid-liquid emulsification systems in stirred batch vessels. The numerical solution techniques are compared based on (i) a breakage dominated system with experimental data available, and (ii) a breakage-coalescence test case. Two numerical approaches are studied for the transient term: (i) time-differencing by a low order finite difference approximation, and (ii) the spectral-element technique. Both approaches use spectral approximations in the phase space dimension. Based on a residual measure, computational costs, and implementation complexity the combined finite difference-spectral approach is recommended above the spectral-in-time-spectral-in-space approach. Within this recommended solution framework, it is not necessary to use a more mathematical complex spectral method than the orthogonal collocation technique.