Due to increasing volatility and decentralisation of the generation, congestion management is becoming increasingly important for distribution grid operation. Therefore, accurate and reliable forecasts are essential for grid operators to maintain grid stability without expensive grid expansion or loss of safety and reliability. Existing approaches are either computationally expensive, have low temporal resolution, or do not quantify the uncertainty in the predictions caused by modelling or the forecast model itself. This study presents a comparison of two uncertainty-aware congestion forecast methods: a neural-network- and a Kalman filter-based approach. First, a PowerFactory-based grid model combined with a Monte Carlo approach is used to generate virtual power measurements. These serve as training data for a multi-layer perceptron, forecasting the expected value and quantiles of the power flows along lines and on transformers. Second, a graph-based abstraction is presented as the basis for a computationally efficient forecast relying on a Kalman filter. The comparison of both alternative methods focuses on the respective forecasting capabilities with respect to uncertainty quantification over variable time windows, as well as the data requirements during the modelling phase. The results demonstrate that both approaches have their merit in different application scenarios with varying requirements.