The benchmark problem of planar contraction flow is often used to evaluate the stability of numerical algorithms and the predictability of viscoelastic constitutive models in predicting the rheological behavior of polymer fluids. In this paper, for the simulation of planar contraction flow, the single/simplified modified double convected Pom-Pom (S-MDCPP) model recently proposed is adopted, and in the frame of iterative stabilized fractional step algorithm, the discrete elastic viscous stress splitting (DEVSS) technique in combination with the streamline upwind Petrov-Galerkin (SUPG) method is taken to serve as a stable numerical solution scheme for the viscoelastic flow, where the equal low-order interpolations are applied to the independent solution variables by virtue of stabilized form of mass conservation equation constructed based-on the finite incremental calculus method. The comparison of rheological behaviors by S-MDCPP model with those by experiment results and DCPP model is taken on the aspects of the material functions of shear viscosities and uniaxial elongation viscosities, stresses fields through the way of flow induced birefringence in the planar contraction flow, with the aim of assessing the constitutive models. In addition, the effects of the constitutive parameters of the S-MDCPP model and Weissenberg number on the rheological behaviors of polymer melts are discussed, with the flow field responses such as velocity, pressure, stress components, and backbone stretch included. Through these comparative studies, the capabilities of the S-MDCPP constitutive model are justified for the applications in branched polymer melts characterizations and numerical modeling.