Path planning plays a vital role in ensuring the safe and efficient navigation of fixed-wing unmanned aerial vehicles (UAVs), particularly in cluttered and complex environments. The increasing demand for autonomous UAV operations highlights the need for reliable algorithms capable of generating optimal and collision-free trajectories. This study addresses the challenge by reviewing recent uses of the Rapidly-exploring Random Tree (RRT) algorithm in various robotic platforms and navigation tasks. The research contribution of this paper is a comparative analysis of RRT and BiRRT for fixed-wing UAV path planning, quantifying trade-offs between path length, computation time, and obstacle clearance using a real-world 2D urban map. This addresses a gap in the literature, as few studies have directly compared these algorithms specifically for fixed-wing UAV surveillance missions. The methods involve implementing both RRT and BiRRT in a simulated environment where each algorithm is evaluated over 100 runs to measure performance metrics such as path length, computation time, and obstacle clearance. A realistic urban map is used to test the algorithms under consistent starting and goal positions. The results show that both RRT and BiRRT achieve a 100% success rate in finding collision-free paths. BiRRT consistently generates shorter paths and requires less computation time, making it more suitable for time-sensitive missions. However, RRT produces safer trajectories with greater average clearance from obstacles, which is advantageous in environments with high collision risk. The findings demonstrate a clear trade-off between safety and efficiency. In conclusion, BiRRT is recommended for missions where speed and efficiency are prioritized, while RRT is better suited for operations emphasizing safety and obstacle avoidance.