What would I benefit most from? Jaw implants or a winged Chin Implant?

What you are asking about are jaw angle implants that can drop the back of the jaw down vertically and add varying degrees of more prominent width (squareness) as desired. They are placed from incisions inside the mouth. Computer imaging will help you decide how much vertical and width of the jaw angles would look best.

Jaw implants are placed at the angle of the mandible to give a more squared jaw look. Chin implants are placed to the front part of the chin and some have extended wings to give added lateral projection to the chin area. The chin and mandible are three-dimensional structure without a full set of photographs, it is impossible to determine what is the best options available.   Best to make appointment with your facial plastic surgeon for an examination and consultation

With just one front view photo, it is hard to say what is best for you.  Sending a front and side view photo will help.  The chin implant will give more projection of your chin (yours looks projected, but can't tell if that is the beard or your chin); the winged sides add a bit of volume to the sides.  The jaw will be the area back at angle of your jaw.  It is possible you may benefit from both.  Photos will help us determine.