This paper studies the fidelity level of the extracted LiDAR (Light Detection And Ranging) building point cloud in relation to the original building. In this context, the building point cloud is compared with a reference model. This comparison allows a deep understanding of the point cloud structure with respect to both the actual building and the constructed model. Consequently, the source of the incompatibility in a (reference or constructed) building model is determined and described. Thus, this study considers four aspects of the building point cloud. First, the errors of building point cloud extraction and the undesirable points are quantified. Hence, it is found that the percentages of undesirable points are sometimes considerable (between 15% and 70%). Second, the evaluation of the fit of the altimetry with the reference model shows that the roof plane equations calculated from LiDAR data can be more precise than those of reference model, Third, the segmentability level between different point densities and building typologies are variable. Finally, the per plane comparison mentions the incompatibility of the plane boundaries of point cloud with reference model. Moreover, considerable differences are noted between the theoretical and the true point densities.