In a variety of engineering applications, metamodels replace detailed computer models in order to reduce the computational effort of simulation processes. Unfortunately, metamodels also degrade the quality of the simulation results. However, no attention has been paid to this trade-off in previous research. Thus, we compare the computational effort and solution quality of a metamodel-based system design. As a use case for this comparison, we define a particular automotive powertrain design task and formulate it as a multi-objective optimization problem with two design objectives and three design variables. First, we solve this use case with a physics-based vehicle model, which is a typical detailed model for powertrain design. Second, we solve the same problem with metamodels. Here, we create several metamodels with different approximation accuracies to analyze the trade-off between computational effort and solution quality. The metamodel solution with the smallest deviation (<1 %) is computed about 9 times faster than the benchmark solution on the target computer used. The fastest metamodel solution is about 42 times faster and causes deviations between 5 % to 10 % compared to the benchmark. This case study can be used to develop metamodel schemes for other applications that provide fast yet accurate solutions. We also demonstrate the practicality of metamodels in real-world system design by comparing the computational effort quantitatively for the first time.