Changepoint problem is, in general, a relatively long and well studied topic in probability and mathematical statistics. There is also an emerging amount of different and practically oriented problems where the changepoint detection and the changepoint estimation play a crucial role. In this paper we particularly focus on the changepoint detection problem within a rather simple panel data model but under relatively complex asymptotics. Different theoretical assumptions are imposed and investigated for such model in the literature—all typically depending on the observational period length and the overall number of available subjects where the first, the second, or both simultaneously are expected to tend to infinity in order to ensure suitable theoretical guarantees. On the other hand, in practical applications, there is always only a limited amount of different subjects and the follow-up period is also quite often restricted. Thus, it is relatively straightforward to choose from the toolbox of different testing procedures if the number of subjects substantially dominates the length of the follow-up period (or vice-versa). However, a kind of hesitation may occur in applications in which both—the number of subjects and the follow-up period length—are roughly of the same magnitude and of relatively small/moderate size. This paper provides a complex comparative simulation study of the changepoint detection tests based on cumulative sums (CUSUM) under different theoretical assumptions (regarding the number of the subjects and the length of the follow-up period) and practically oriented recommendations drawn from the results are summarized at the end.