ESD wrist strap stud size?
No, the size of the stud is not going to make an electrical difference. The reason is on most wrist straps there is a 1MΩ resistor in series along the strap cable. The contact resistance is going to be much much lower, less than a tenth of an ohm. There might be mechanical differences, but these would be a matter of preference. 

From the Antistatic strap wiki:


  Wrist straps designed for industrial use usually connect to earth bonding points, ground connections built into the workplace, via either a standard 4 mm plug or 10 mm press stud, whereas straps designed for consumer use often have a crocodile clip for the ground connection.