Unmanned Aerial Vehicles (UAVs) have been very effective in collecting aerial images data for various Internet-of-Things (IoT)/smart cities applications such as search and rescue, surveillance, vehicle detection, counting, intelligent transportation systems, to name a few. However, the real-time processing of collected data on edge in the context of the Internet-of-Drones remains an open challenge because UAVs have limited energy capabilities, while computer vision techniquesconsume excessive energy and require abundant resources. This fact is even more critical when deep learning algorithms, such as convolutional neural networks (CNNs), are used for classification and detection. In this paper, we first propose a system architecture of computation offloading for Internet-connected drones. Then, we conduct a comprehensive experimental study to evaluate the performance in terms of energy, bandwidth, and delay of the cloud computation offloading approach versus the edge computing approach of deep learning applications in the context of UAVs. In particular, we investigate the tradeoff between the communication cost and the computation of the two candidate approaches experimentally. The main results demonstrate that the computation offloading approach allows us to provide much higher throughput (i.e., frames per second) as compared to the edge computing approach, despite the larger communication delays.