The trade-off between language expressiveness and system scalability (E&S) is a well-known problem in RDF stream reasoning. Higher expressiveness supports more complex reasoning logic, however, it may also hinder system scalability. Current research mainly focuses on logical frameworks suitable for stream reasoning as well as the implementation and the evaluation of prototype systems. These systems are normally developed in a centralized setting which suffer from inherent limited scalability, while an in-depth study of applying distributed solutions to cover E&S is still missing. In this paper, we aim to explore the feasibility of applying modern distributed computing frameworks to meet E&S all together. To do so, we first propose BigSR, a technical demonstrator that supports a positive fragment of the LARS framework. For the sake of generality and to cover a wide variety of use cases, BigSR relies on the two main execution models adopted by major distributed execution frameworks: Bulk Synchronous Processing (BSP) and Record-at-A-Time (RAT). Accordingly, we implement BigSR on top of Apache Spark Streaming (BSP model) and Apache Flink (RAT model). In order to conclude on the impacts of BSP and RAT on E&S, we analyze the ability of the two models to support distributed stream reasoning and identify several types of use cases characterized by their levels of support. This classification allows for quantifying the E&S trade-off by assessing the scalability of each type of use case \wrt its level of expressiveness. Then, we conduct a series of experiments with 15 queries from 4 different datasets. Our experiments show that BigSR over both BSP and RAT generally scales up to high throughput beyond million-triples per second (with or without recursion), and RAT attains sub-millisecond delay for stateless query operators.