Tooth extraction took place 4 months ago. Would a radiograph or a 3d CT be best for a specialist to view a broken bony tooth wall (s)?

Eval Bony socket. If you did not have a bone graft at the time of your extraction, you may assume that there has been a lateral and vertical collapse of bone dimensions at that site, sometimes as much as 50%! i would immediately have a bone graft done to augment both dimensions prior to having an implant placed!
Cone Beam CT. A cone beam ct will provide more information to evaluate the extraction site and any defects present.
Not radiograph. It would be very unlikely to be able to find it with a regular radiograph. You might see it in the ct scan. Are you waiting for the area to heal before placing an implant? Was the area bone grafted at the time of extraction? If so, there probably won't be any sign of it.