When you parent one thing to another it can often shift the location of the child because it is essentially changing its positional frame of reference to the parent. So in most cases it needs to be re-positioned due to the new frame of reference. A way to do this is to position the hairpiece where it needs to be before doing the parenting, then set the 3D cursor to the hairpiece’s object center, then do the parenting (hairpiece re-locates, possibly even out of view), then set the hairpiece’s location to the 3D cursor, bringing the hairpiece back home. This can all be done using the SHIFT+S options for snapping.
It’s also usually a good idea to Apply Scale and Rotation to the hairpiece before parenting.
Parenting the hairpiece to the head bone is a good method (if your model/armature allows this), as long as the hairpiece will always stay on the head. The Child Of constraint is useful if you need to animate the influence of the parent, not usually the case for a wig/hairpiece.