Accurate daily rainfall forecasting is essential for water resource management, flood risk mitigation, and early warning systems in tropical mountain regions. This study systematically compared five univariate forecasting models drawn from three methodological families—one statistical model (ARIMA), two deep learning architectures (Long Short-Term Memory, LSTM; Gated Recurrent Unit, GRU), and two decomposition-based hybrid models (Discrete Wavelet Transform–LSTM, DWT-LSTM; Variational Mode Decomposition–GRU, VMD-GRU)—for one-step-ahead daily rainfall forecasting across 18 meteorological stations in Tungurahua Province, Ecuador, covering the period 2013–2025. Model performance was evaluated using a comprehensive multi-metric framework that combined continuous accuracy metrics (Mean Absolute Error, MAE; Root Mean Square Error, RMSE; Nash-Sutcliffe Efficiency, NSE; Kling-Gupta Efficiency, KGE) and categorical event-detection metrics (Probability of Detection, POD; False Alarm Ratio, FAR; Critical Success Index, CSI) applied at three precipitation thresholds (1 mm, P90, and P95). LSTM achieved the best overall performance for continuous prediction and rainfall-occurrence detection at the 1 mm threshold; GRU delivered comparable skill at lower computational cost, making it a practical alternative for operational applications. Station-level performance rankings varied considerably across the network, reflecting strong hydroclimatic heterogeneity and confirming that spatially uniform single-model forecasting strategies are suboptimal. All evaluated models failed to reliably detect high-intensity (P90) and extreme (P95) rainfall events, producing very low POD and high FAR values. Although ARIMA ranked first in relative terms for extreme-event detection, its absolute skill remained insufficient for operational purposes. Hybrid decomposition models (DWT-LSTM, VMD-GRU) did not outperform the simpler recurrent architectures and frequently produced negative NSE values. These results demonstrate that univariate approaches are adequate for routine daily rainfall forecasting but inadequate for reliable extreme-event prediction, underscoring the critical need for multivariate predictor frameworks, specialized loss functions, and probabilistic approaches in future research.