Once a character successfully starts grappling a target, is there now any difference between the aggressor and the defender? Or do both characters get exactly the same mechanical effects, such as no dex bonus to AC, no threatened squares, etc.?
The various rules of the grapple maneuver repeatedly refer to whether or not you are grappling, not who grappled who:
Perhaps most tellingly:
There are exceptions, however. Improved Grab, for instance, has the following: