Automated classification of organisms to species based on their vocalizations would contribute tremendously to abilities to monitor biodiversity, with a wide range of applications in the field of ecology. In particular, automated classification of migrating birds' flight calls could yield new biological insights and conservation applications for birds that vocalize during migration. In this paper we explore state-of-the-art classification techniques for large-vocabulary bird species classification from flight calls. In particular, we contrast a 'shallow learning' approach based on unsupervised dictionary learning with a deep convolutional neural network combined with data augmentation. We show that the two models perform comparably on a dataset of 5428 flight calls spanning 43 different species, with both significantly outperforming an MFCC baseline. Finally, we show that by combining the models using a simple late-fusion approach we can further improve the results, obtaining a state-of-the-art classification accuracy of 0.96.