Should I add plywood or OSB between sistered beams?
There is no real reason to put a spacer between the joists when sistering them.  Usually using some 1/2 plywood between dimensional lumber is to correct the thickness to vertical lumber dimensions, like on a header over a door.  If you were to add a spacer, I would use plywood as OSB has much less sheer strength.  Adding some plywood will add a bit more strength, but in your case, may not make a difference.