This article addresses the automatic detection of vocal, nocturnally migrating birds from a network of acoustic sensors. Thus far, owing to the lack of annotated continuous recordings, existing methods had been benchmarked in a binary classification setting (presence vs. absence). Instead, with the aim of comparing them in event detection, we release BirdVox-full-night, a dataset of 62 hours of audio comprising 35402 flight calls of nocturnally migrating birds, as recorded from 6 sensors. We find a large performance gap between energy-based detection functions and data-driven machine listening. The best model is a deep convolutional neural network trained with data augmentation. We correlate recall with the density of flight calls over time and frequency and identify the main causes of false alarm.