The facial nerve provides motion to the muscles of the face and some in the neck as well. Since the facial nerve runs in the region of any facelift surgery, injury is possible. Fortunately, the risk of injury is lower the 1% and any injury is usually temporary. Risk is similar for deep plane facelift surgery and also very unlikely to have any permanent injury.
At the end of the day, the person performing your surgery is more important then the technique used. It is important that you choose a skilled facelift surgeon who performs deep plane facelifts often (every week). Most surgeons that perform a Deep Plane Facelift surgery have significant experience performing surgery of the face, which minimizes the chance of risk. During your consultation ask your surgeon how often they perform facelifts and ask them if they have ever had a facial nerve injury.