In cloud event processing, data generated at the edge is processed in real-time by cloud resources. Both distributed stream processing (DSP) and Function-as-a-Service (FaaS) have been proposed to implement such event processing applications. FaaS emphasizes fast development and easy operation, while DSP emphasizes efficient handling of large data volumes. Despite their architectural differences, both can be used to model and implement loosely-coupled job graphs. In this paper, we consider the selection of FaaS and DSP from a cost perspective. We implement stateless and stateful workflows from the Theodolite benchmarking suite using cloud FaaS and DSP. In an extensive evaluation, we show how application type, cloud service provider, and runtime environment can influence the cost of application deployments and derive decision guidelines for cloud engineers.