I can't really answer the question about different thicknesses...
But, I tend to use fishing line, monofilament not braided, of 0.11 mm thickness for all my rigging in both 1/48 and 1/32 scale. That means a real life thickness of 5.28 and 3.52 mm respectively. Along Andreas' line of thought I too don't believe that small differences in real life will be visible in small scale modelling.
Good luck with the rigging!
/Fredrik