I have a recessed chin and open bite malocclusion. Should I get a chin implant or a sliding genioplasty to help my appearance?

Without an exam your question cannot
be answered.  You will need to see an Oral/Maxillofacial surgeon to see
if othognathic surgery, genioplasty or using an implant is best for your
specific case. It should be noted that patients with severely weak jaws
or abnormally functioning jaws may be better treated with other facial
surgery (orthognathic surgery), although a chin augmentation may be an
option at a later time. These patients should seek the advice of a
plastic surgeon to determine which course is right for them. Here is
some information to help you make this decision: Candidates for Chin
Augmentation - Patients whose chin profiles are weak but have normally
functioning jaws are candidates for Chin Augmentation. Many of these
candidates have used injectable fillers in the past to strengthen the
protrusion of their chins, but are looking for a permanent solution. If
you are one of these patients, then you are a likely candidate for chin
augmentation
#weakchin #chinimplant

 A chin implant is performed purely for cosmetic purposes will not  make any improvements to the way the teeth fit together.  It simply augments the chin  Forward and is performed under local anesthesia as an outpatient procedure. When there is a combination of her recessive chin and malocclusion with the teeth not fitting together properly,  consider a sliding genioplasty performed by an oral surgeon. For many examples of just chin implants, please see the link and the video below

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  From the photos, your chin is quite weak with some excess fat and skin under the chin.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess fat and skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.   Neither the chin implant nor the sliding genioplasty will affect (improve) your bite.  This would require orthognathic intervention.  Similarly, orthognathic intervention will not provide the necessary forward chin projection to correct the weak chin.  They are both specific to their respective areas of improvement.
Hope this helps.

Your growth pattern necessitates a genioplasty due to the inability to get the lips together naturally, the slope of the jawline, and the area under the chin. You should also consider the orthodontics/jaw surgery combination since  good oral health will prevent the loss of teeth you suggested.