This article presents an extensive comparison of collision avoidance systems with local path planning based on a mathematical model of an autonomous underwater vehicle (AUV) controlled by the trajectory tracking control system. In the study, six methods such as improved artificial potential field (APF), D* algorithm, dynamic course adjustment (DCA), genetic algorithm (GA), particle swarm optimization (PSO) and rapidly-exploring random tree (RRT) were tested, the efficiency of which was verified on 10 test maps with various types of obstacles' configurations and shapes with taking into account real-time decision-making ability. Both obstacle detection system and collision avoidance systems were extensively fine-tuned to achieve a compromise between collision avoidance efficiency and minimization of computation time. Based on the prepared simulation framework and environment, the trajectory completion percentage, average trajectory deviation, trajectory energy consumption, computation time and percentage of collision trials were assessed. The best results in terms of AUV safety were achieved by the D* and DCA methods. Slightly worse results were obtained by GA and PSO. Considering real-time decision-making ability, the best results were obtained by DCA and APF methods. Based on a detailed analysis of the results, it can be concluded that the DCA method can be used in quick-react emergency systems, and D*, GA and PSO methods are reasonable to use in medium-range local collision avoidance systems.