Additive manufacturing techniques are increasingly used in industry. However, the direct usage of additively manufactured parts is limited due to their relatively low surface quality. Especially to achieve functional surfaces, post-processing has to be carried out. Post-processing methods include traditional mechanical cutting processes as well as electrical and chemical processes. Since previously deposited material is removed and additional manufacturing time is necessary, post-processing leads to increased manufacturing costs. Therefore, if additive manufacturing is to be competitive with traditional manufacturing processes, choosing the correct post-processing method is vital. Decision parameters, for example, are the achievable surface quality, the amount of material removal, and the preservation of the shape. In this article, the suitability of two traditional manufacturing processes, milling and mass finishing, as post-processing methods for parts from 316L, manufactured with powder bed fusion using a laser beam, is described. It is characterized how the depth of material removal influences the surface quality. For the milling process, it is determined that a depth of material removal of 0.2 mm leads to a stable surface quality. Finally, the processes' effectiveness as post-processing methods is assessed by comparing the achievable surface quality, showing that mass finishing processes are an economic post-processing option in specific cases.