In the literature, there are a small number of publications regarding the construction and application of machine tools that integrate several machining operations. Additionally, solutions that allow for such integration for complex operations, such as the machining of shape surfaces with complex contours, are relatively rare. The authors of this article carried out dimensional analysis of workpieces machined using a prototype Computerized Numerical Control (CNC) machine tool that integrates the possibilities of 3D scanning, milling operations in three axes, and grinding operations using abrasive discs. The general description of this machine tool with developed methodology and the most interesting results obtained during the experimental studies are given. For a comparative analysis of the influence of the machining method on the geometric accuracy of the test pieces, an Analysis of Variance (ANOVA) was carried out. The obtained results show that for four considered features (deviations of flatness, vertical parallelism, opening dimensions, and opening cylindricality), no statistically significant differences were detected. For the evaluation criteria, the probability level p exceeded the assumed confidence level α = 0.05 and ranged from p = 0.737167 to p = 0.076764. However, such differences were found for two others—a dimensional deviation between flat surfaces (p = 0.010467) and horizontal parallelism deviation (p = 0.0)—as well as for the quality of the machined surface defined by four surface texture parameters: Ra (p = 0.831797), Rt (p = 0.759636), Rq (p = 0.867222), and Rz (p = 0.651896). The information obtained by the ANOVA will be useful for the elimination the weaknesses of the prototype machine tool, further analysis of technological strategies, and to find possible benefits of integrating machining operations.