The long and short of it is that the way bones are displayed in Wireframe view in both Pose and Edit modes has changed from 2.79 to 2.8 and following versions. Instead of being just a wireframe, they are now semi-opaque. Example below:
In addition to this visual change, there is also a functional change: You can no longer select objects ‘through’ these semi-opaque wireframe bones with the eyedropper tool, when for example picking targets for constraints.
Is there any way to restore the appearance and function of wireframe for bones from 2.79?