A generative model is a statistical model that is able to generate new data instances from previously observed ones. In the context of business processes, a generative model creates new execution traces from a set of historical traces, also known as an event log. Two families of generative process simulation models have been developed in previous work: data-driven simulation models and deep learning models. Until now, these two approaches have evolved independently and their relative performance has not been studied. This paper fills this gap by empirically comparing a data-driven simulation technique with multiple deep learning techniques, which construct models are capable of generating execution traces with timestamped events. The study sheds light into the relative strengths of both approaches and raises the prospect of developing hybrid approaches that combine these strengths.