strange - both of the normal maps look the same
I am curious, what happens, if you export your fbx from modo with "save smoothing groups" on?
please don´t think I am ignoring your explanation, but if I look at the comparison at the bottom of your image, between the left and the right image - it really looks to me as if the left cubes show one single smoothing group (smooth), while the cubes on the right side have separate smoothing groups for each face (faceted)
I imported your cubetest_lo.fbx into 3dsMax - and the faces don´t have smoothing groups assigned. Different engines interpret faces without smoothing groups in different ways: some engines display them as faceted (separate smoothing groups), while other engines display them as smooth (single smoothing group)
btw, why does the shader on the left side look different from the shader on the right side (the left one looks way more reflective)?
So i still would be tempted to think, that your issue has nothing to do with the normal maps