Test suite reduction strategies aim to produce a smaller and representative suite that presents the same coverage as the original one but is more cost-effective. In the modelbased testing (MBT) context, reduction is crucial since automatic generation algorithms may blindly produce several similar test cases. In order to define the degree of similarity between test cases, researchers have investigated a number of distance functions. However, there is still little or no knowledge on whether and how they influence on the performance of reduction strategies, particularly when considering MBT practices. This paper investigates the effectiveness of distance functions in the scope of a MBT reduction strategy based on the similarity degree of test cases. We discuss six distance functions and apply them to three empirical studies. The first two studies are controlled experiments focusing on two real-world applications (and real faults) and ten synthetic specifications automatically generated from the configuration of each application (and faults randomly generated). In the third study, we also apply the reduction strategy to two subsequent versions of an industrial application by considering real faults detected. Results show that the choice of a distance function has little influence on the size of the reduced test suite. However, as reduced suites are different depending on the distance function applied, the choice can significantly affect the fault coverage. Moreover, it can also affect the stability of the reduction strategy regarding coverage of different sets of faults on different executions.