I think I need to have more details. If I open any of your files in V6, 3dm or obj, they look fine. By that I mean I’m not seeing anything weird like you show in your V6 image. Anyone watching this thread please try it for yourself and report here if you see anything odd.
Having said that, there is clearly a difference in mesh settings because the obj file saved from V6 is roughly 5 times larger and both files have textures and normals. I did notice in your V6 file that you must have one of the radios selected that writes out the mesh in a special way. Normally, obj files written from Rhino will have the same index number for the vertex, normal and texture. Your normal and texture are the same but your vertex doesn’t match. I don’t think this is a problem, it read in fine for me, but you might make sure you have vertex welding set to unmodified if you want it to be more like the V4 file. Your file looks like you had set to welded.
Since OBJ is old format both versions of Rhino should be able to open any obj file you produce. It would be interesting to know if you see the same ugliness in both versions importing the file exported from V6.
At this point I can’t tell what the problem might be, whether it’s export, import or isolated to your computer. I guess the next step might be to give me pictures of the obj and mesh settings you’re using in the 2 versions to save your files.