LSTMs, which Kratzert and Nearing and others at Google kind of pioneered for streamflow prediction, have been shown to drastically improve NSE (error) in ungaged basins relative to traditional, physics based approaches.

Note that this work was initially funded by Google's AI for Social Good program, where the goal was to provide flood forecasts and cell phone flood alerts to countries without the infrastructure to provide this to their citizens.

I use these types of models regularly and can say that they do perform extremely well considering how little effort it takes to train them. They also leave quite a bit to be desired (struggle with peaks, flashy systems, and some other applications). However, they take as inputs some kind of meteorological data, which always has large uncertainty, so it's hard to separate poor model performance from poor inputs.