Classical molecular dynamics (MD) calculations represent a significant part of the utilization time of high-performance computing systems. As usual, the efficiency of such calculations is based on an interplay of software and hardware that are nowadays moving to hybrid GPU-based technologies. Several well-developed open-source MD codes focused on GPUs differ both in their data management capabilities and in performance. In this work, we analyze the performance of LAMMPS, GROMACS and OpenMM MD packages with different GPU backends on Nvidia Volta and AMD Vega20 GPUs. We consider the efficiency of solving two identical MD models (generic for material science and biomolecular studies) using different software and hardware combinations. We describe our experience in porting the CUDA backend of LAMMPS to ROCm HIP that shows considerable benefits for AMD GPUs comparatively to the OpenCL backend.