Inverse and acceptance–rejection strategy are two widely used schemes by various Monte Carlo (MC) methods for handling particle coagulations. They exhibit different algorithm complexity and computational efficiency. In an effort to have a better understanding of the two schemes, we systematically compare their computational performance on CPU and GPUs (graphic processing units) with different computing conditions. The obtained results may serve as a useful guidance on the choice of the particular scheme by various MC methods for handling problems of particle dynamics in practice. Display omitted •The computational performances of MCs using Inverse and AR scheme are compared.•AR scheme has an obvious edge over Inverse scheme both on CPU and GPU.•In particular, AR performs much better than its counterpart for multi-cells cases.•Practically, AR is a better choice for MCs in solving particle dynamic problems.