Metaheuristics are successful algorithmic concepts to tackle extit{NP}-hard combinatorial optimization problems. In this paper we deal with metaheuristics for the K-cardinality tree (KCT) problem in edge-weighted graphs. This problem has several applications, which justify the need for efficient methods to obtain good solutions. There are already metaheuristic approaches to tackle the KCT problem to be found in the literature. However, there is a lack of benchmark problem instances and therefore also a lack of comparison between these approaches. Moreover, studies comparing metaheuristic approaches -- for whatever combinatorial optimization problem -- often suffer from the fact that they compare results obtained on different processors, on program code implemented in different programming languages and based on different data structures. In contrast to these studies, we aim for a fair comparison of three different metaheuristic approaches. We compare these approaches on a carefully chosen set of benchmark instances characterized by several distinguishing features. Our results show, that due to the different characteristics of different areas of the problem instance space none of our metaheuristic approaches can be identified as the best metaheuristic approach. It is rather the case that each approach has its advantages for certain areas of the problem instance space.