Edge Computing harnesses resources close to the data sources to reduce end-to-end latency and allow real-time process automation for verticals such as Smart City, Healthcare and Industry 4.0. Edge resources are limited when compared to traditional Cloud data centres; hence the choice of proper resource management strategies in this context becomes paramount. Microservice and Function as a Service architectures support modular and agile patterns, compared to a monolithic design, through lightweight containerisation, continuous integration / deployment and scaling. The advantages brought about by these technologies may initially seem obvious, but we argue that their usage at the Edge deserves a more in-depth evaluation. By analysing both the software development and deployment lifecycle, along with performance and resource utilisation, this paper explores microservices and two alternative types of serverless functions to build edge real-time IoT analytics. In the experiments comparing these technologies, microservices generally exhibit slightly better end-to-end processing latency and resource utilisation than serverless functions. One of the serverless functions and the microservices excel at handling larger data streams with auto-scaling. Whilst serverless functions natively offer this feature, the choice of container orchestration framework may determine its availability for microservices. The other serverless function, while supporting a simpler lifecycle, is more suitable for low-invocation scenarios and faces challenges with parallel requests and inherent overhead, making it less suitable for real-time processing in demanding IoT settings.