Generative deep learning (DL) models have been successfully adopted for vulnerability patching. However, such models require the availability of a large dataset of patches to learn from. To overcome this issue, researchers have proposed to start from models pre-trained with general knowledge, either on the programming language, or on similar tasks such as bug fixing. Other alternatives, not investigated in this context yet, foresee the use of prompt tuning, i.e., transforming the fine-tuning instances to better exploit the knowledge acquired during pre-training. Despite the efforts in the area of automated vulnerability patching, there is a lack of systematic studies on how these different training procedures impact the performance of DL models for such a task. This paper provides a manyfold contribution to bridge this gap, by (i) comparing existing solutions of self-supervised and supervised pre-training for vulnerability patching; and (ii) for the first time, experimenting with different kinds of prompt-tuning for this task. The study required to train/test 23 DL models. We found that a supervised pre-training focused on bug-fixing, while expensive in terms of data collection, substantially improves DL-based vulnerability patching. When applying prompt tuning on top of this supervised pre-trained model, there is no significant gain in performance. Instead, prompt-tuning is an effective and cheap solution to substantially boost the performance of self-supervised pre-trained models, i.e., those not relying on the bug-fixing pre-training.