The present study concentrates on the generality of selection hyper-heuristics across various problem domains with a focus on different heuristic sets in addition to distinct experimental limits. While most hyper-heuristic research employs the term generality in describing the potential for solving various problems, the performance changes across different domains are rarely reported. Furthermore, a hyper-heuristic's performance study purely on the topic of heuristic sets is uncommon. Similarly, experimental limits are generally ignored when comparing hyper-heuristics. In order to demonstrate the effect of these generality related elements, nine heuristic sets with different improvement capabilities and sizes were generated for each of three target problem domains. These three problem domains are home care scheduling, nurse rostering and patient admission scheduling. Fourteen hyper-heuristics with varying intensification/diversification characteristics were analysed under various settings. Empirical results indicate that the performance of selection hyper-heuristics changes significantly under different experimental conditions.