We study real-time motion planning in dynamic hazard fields through a controlled comparison between classical planning and learning-based methods. Rather than introducing a new planner, we construct a unified benchmark in which representative classical and learning-based methods face the same environments, motion constraints, information assumptions, and evaluation metrics. The test environment consists of planar domains populated with rotating sprinkler-like hazards that generate time-varying forbidden regions via sweeping angular sectors. Our results show a clear regime shift. In deterministic environments, classical planners achieve near-perfect success and higher-quality paths, though sometimes at the cost of substantial planning or replanning time. Under stochastic obstacle dynamics, however, online search becomes strongly budget-sensitive: low budgets lead to frequent failure, while high budgets improve success at the cost of latency and longer trajectories. PPO-based policies, trained under the same scenario distribution, consistently outperform in latency, success rate, and path quality in these stochastic regimes. Overall, the results indicate that uncertainty in obstacle evolution, more than partial observability, is the dominant factor determining which planning paradigm is practically effective for the problem at hand.