Combining Mixed Reality (MR) and Building Information Modeling (BIM) facilitates the projection of virtual BIM data into real construction settings, enabling on-site, real-time monitoring of construction progress and quality. However, current approaches are largely based on human observation to spot differences between the projected BIM model and the actual state on site. Inspecting complex structures, such as Mechanical, Electrical, and Plumbing (MEP) systems, continues to be a difficult task, prone to human error and requiring substantial time. Automation in detecting deviations can streamline and expedite the inspection process. In pursuit of this objective, this document details and reviews four separate algorithms for mesh-to-mesh comparison, targeting the identification and quantification of discrepancies between the 3D mesh obtained on site via MR systems and the mesh geometry of the elements in the BIM model as envisioned.