Modeling of coherent polarized light propagation in turbid scattering medium by the Monte Carlo method provides an ultimate understanding of coherent effects of multiple scattering, such as enhancement of coherent backscattering and peculiarities of laser speckle formation in dynamic light scattering (DLS) and optical coherence tomography (OCT) diagnostic modalities. In this report, we consider two major ways of modeling the coherent polarized light propagation in scattering tissue-like turbid media. The first approach is based on tracking transformations of the electric field along the ray propagation. The second one is developed in analogy to the iterative procedure of the solution of the Bethe-Salpeter equation. To achieve a higher accuracy in the results and to speed up the modeling, both codes utilize the implementation of parallel computing on NVIDIA Graphics Processing Units (GPUs) with Compute Unified Device Architecture (CUDA). We compare these two approaches through simulations of the enhancement of coherent backscattering of polarized light and evaluate the accuracy of each technique with the results of a known analytical solution. The advantages and disadvantages of each computational approach and their further developments are discussed. Both codes are available online and are ready for immediate use or download.