A couple things:
1) Reinforcement rods are not round - there's no diameter. As you're primarily trying to increase stiffness in the vertical direction, they are made taller than they are wide. They are rectangular, which means you route a slot for them, and when glued in, they are locked in place.
2) Making a reinforcement rod bigger is not necessarily an improvement - you are limited by the dimensions of the neck - make them too tall or too wide, and the wood parts get too thin, putting weak spots in a neck - there is only so much you can do to stiffen a neck before you've gone too far.
3) OK, 3 things - reinforcement rods aren't really about strength - they are there to provide stiffness. Yes, there is a difference.