"Unfortunately I can't run a triangel volume on your surfaces. My report window is not displaying so I can not tell you the result of the Generate Inferred Breakline command."
Paul, the reason you are not getting the Report to open is due to the Surface Properties > Description on each of the surfaces. Since we are working in the English version of the product, the character for the description cannot be read by the program. Therefore I just deleted the description from both surfaces and then the Triangle Volumes report works.
I agree with Paul I believe if you only bring over the triangles you will get a much closer triangle volumes value between InRoads and Civil3D.