Accurate streamflow forecasting is essential for effective water resource management, flood mitigation, and environmental conservation. We present a comparative analysis of three streamflow forecasting models applied to an Italian natural catchment, the Posina River basin. The ARIMAX model extends the traditional ARIMA approach by incorporating exogenous variables, while the LSTM model, a type of recurrent neural network, is designed to capture complex temporal dependencies in time series data. The physical-based continuous model was developed with HEC-HMS software and is based on the Soil Moisture Accounting model, combined with the Clark Unit Hydrograph Model for runoff transformation and a Linear Reservoir Model for baseflow recessions. We utilized a dataset of hourly hydrological data from the Posina River basin, covering nearly 13 years. The models' performances were evaluated using Nash-Sutcliffe Efficiency, Kling-Gupta Efficiency, and Mean Absolute Error as metrics. Results indicate that LSTM and traditional physical-based models outperform the ARIMAX model in predicting streamflow, particularly in capturing peak flows and overall trends. However, the LSTM model tends to smooth out rapid changes in streamflow, while the traditional physical-based model occasionally overestimates peak values. This research highlights the strengths and limitations of each model in hourly streamflow forecasting. We suggest that the choice of model should be tailored to the specific needs of the forecasting task. The LSTM recurrent neural network, more than the ARIMAX model, represents a convenient approach for streamflow forecasting as an alternative to the traditional physical-based hydrological model since it guarantees excellent results with an easier calibration process.