We examine the accuracy and performance of several leading discrete-element-modeling approaches to predicting equilibrium and dynamic rheological properties of an aqueous, polystyrene suspension. What distinguishes each approach presented is the methodology of handling the solvent hydrodynamics. Specifically, we compare stochastic rotation dynamics (SRD), fast lubrication dynamics (FLD), and dissipative particle dynamics (DPD) methods of including solvent hydrodynamics against each other and against experimental data. Quantities examined are equilibrium structure properties (e.g., pair-distribution function), equilibrium dynamic properties (e.g., long-time diffusivities), and dynamic response (e.g., steady shear). In all approaches, we deploy the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential for colloid-colloid interactions. Comparisons are made over a range of volume fractions and salt concentrations. Long-time diffusivities are especially difficult to compute and exhibit clear discrepancies across methods. Significant effort is devoted in this paper to explain the reasons for the observed inconsistencies. Shear viscosities are predicted to within experimental and numerical error estimates with both SRD and FLD methods, while traditional DPD proves to be too inefficient to be useful in this regard. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.3690105]