Side-channel attacks aim to recover cryptographic secrets by exploiting involuntary information channels coming from the computational platform of the targeted cipher implementation, e.g., power consumption or electromagnetic emissions. Among them deep learning based attacks have recently obtained great attention from both industry and academia, due to their greater efficiency and accuracy with respect to other methodologies. We provide a systematic comparison of the effectiveness of deep learning based attacks by considering different data acquisition and training methods. We also tackle the problem of the portability of the derived information leakage model, by analysing multiple instances of the same device, an ARM Cortex-M4 32-bit processor, running a software implementation of the AES-128 cipher. We complement the exploration of the attack space by considering datasets corresponding to cipher executions employing, for each run, either the same fixed secret key or a randomly chosen one. Furthermore, we generalize the set of inputs considered to build the model, by adding also the plaintexts fed to each cipher run. Finally, from the perspective of efficiency, we point out several unexpected and counterintuitive benchmark points.