Hey Joe, that's my two cents. For pulling and/curling movements, grip strength is the limiting factor, so this is obvious. However, in pressing, grip strength is not as much since the prime movers are the pecs. HOwever, EMG tests with thinner bars on benchpress had the greatest recruitment in the forearms. This might be due to the lifting styles, I know some that will grip the bar has hard as possible, as with the thick bar, it's harder to do so. Stability and wrist might also be a limiting factor.
https://www.ncbi.nlm.nih.gov/pubmed/17313296