Unmanned aerial vehicle (UAV) usage is expected to surge in the coming decade, raising the need for heightened security measures to prevent airspace violations and security threats. This study investigates deep learning approaches to UAV classification focusing on the key issue of data scarcity. To investigate this we opted to train the models using a total of 4,500 seconds of audio samples, evenly distributed across a 9-class dataset. We leveraged parameter efficient fine-tuning (PEFT) and data augmentations to mitigate the data scarcity. This paper implements and compares the use of convolutional neural networks (CNNs) and attention-based transformers. Our results show that, CNNs outperform transformers by 1-2\% accuracy, while still being more computationally efficient. These early findings, however, point to potential in using transformers models; suggesting that with more data and further optimizations they could outperform CNNs. Future works aims to upscale the dataset to better understand the trade-offs between these approaches.