This study compares two methodological approaches for predicting, at a given site, threshold exceedances of atmospheric variables such as temperature and wind speed: (i) direct probabilistic methods, which treat exceedance as a binary classification problem, and (ii) full distribution probabilistic methods, which model the complete conditional probability law of the target variable. Using theoretical analysis and numerical simulations on a toy model, alongside real-world data from the MeteoNet dataset (2016--2018) for southeastern France, we demonstrate that the full distribution approach consistently outperforms the direct method for rare, extreme events. This advantage arises because the full distribution approach effectively learns the parameters of the conditional distribution from moderate and mild intensity events, thereby achieving better calibration and discrimination in the tails. We find that the specific parametric shape of the chosen distribution plays a secondary role compared to accurately capturing predictable shifts in its bulk properties (i.e., mean and variance). This empirical indistinguishability is also informative about the physical mechanics driving atmospheric extremes, suggesting that extreme exceedances are primarily driven by significant conditional displacements of the entire distribution rather than by unpredictable, fat-tailed anomalies within a static climatology. Our results are validated for both strong surface wind speeds and intense hourly rainfall, with performance evaluated using proper scoring rules (Brier score, logarithmic score) and deterministic skill scores (Peirce Skill Score, CSI, HSS). These findings highlight the critical importance of modeling the full probability distribution for rare-event forecasting and provide practical guidance for improving extreme weather prediction in operational meteorology.