I don't really know 3D in PS either but I do know that OBJ files can be a right pain!
I exported a 3d model from 3dsMax as an obj, imported it into PS and it was fine.....but I think that was more luck than judgement to be honest.
I've also exported OBJ files for 3rd party UV unwrapping and it wasn't so successful first time which meant I had to work out what the problem may be....hence the suggestions below are based on that scenario and not importing into PS.
There where a couple of things that I had to 'fix' before exporting the obj file:
1. Alignment:
The alignment of the model to the 'world' coordinate system....anything else and the model would not be aligned when imported.
2. Normals:
It wasn't really a problem at the time but some, or all, of the normals could be flipped.
This would result in a model very similar to your example....especially if there is any 'smoothing' (as in smoothing groups) applied.
3. The 'Z' axis:
You can change the orientation of the 'z' axis on export.
Different programs will need a different reference for the 'z' axis......what that will be is pure guesswork until you select the right one.....but at least it can only be one of three so its not too bad.
I'm assuming you created the model in 'Blender' which is not something I've ever used so cannot be any more specific than the above....sorry.
So...check the model alignment to the world axis, check the normals and see if you can change the 'z' axis when exporting to an OBJ file.
Regards.
MrTom.
