This study evaluates and compares the computational performance and practical applicability of advanced path planning algorithms for Unmanned Aerial Vehicles (UAVs) in dynamic and obstacle-rich environments. The Adaptive Multi-Objective Path Planning (AMOPP) framework is highlighted for its ability to balance multiple objectives, including path length, smoothness, collision avoidance, and real-time responsiveness. Through experimental analysis, AMOPP demonstrates superior performance, with a 15% reduction in path length compared to A*, achieving an average path length of 450 m. Its angular deviation of 8.0° ensures smoother trajectories than traditional methods like Genetic Algorithm and Particle Swarm Optimization (PSO). Moreover, AMOPP achieves a 0% collision rate across all simulations, surpassing heuristic-based methods like Cuckoo Search and Bee Colony Optimization, which exhibit higher collision rates. Real-time responsiveness is another key strength of AMOPP, with an average re-planning time of 0.75 s, significantly outperforming A* and RRT*. The computational complexities of each algorithm are analyzed, with AMOPP exhibiting a time complexity of O(k·n) and a space complexity of O(n), ensuring scalability and efficiency for large-scale operations. The study also presents a comprehensive qualitative and quantitative comparison of 14 algorithms using 3D visualizations, highlighting their strengths, limitations, and suitable application scenarios. By integrating weighted optimization with penalty-based strategies and spline interpolation, AMOPP provides a robust solution for UAV path planning, particularly in scenarios requiring smooth navigation and adaptive re-planning. This work establishes AMOPP as a promising framework for real-time, efficient, and safe UAV operations in dynamic environments.