Doctors are studying this question. A closed release is done with an arthroscope. This tool allows the doctor to go through the skin and into the joint with only a puncture hole. A tiny TV camera on the end allows the doctor to see inside the area. An open release involves a cut or incision to open the skin, muscle, and joint. In both operations, the tendon is released and then repaired and reattached.
A recent report suggests there's no difference between these two methods in the long-run. Short-term results may be the key. In a study of 87 patients (54 open, 33 closed), results were the same after two years. But the arthroscopic group started rehab and went back to work sooner than the open group. The open group also needed more therapy after the operation.
The small number of patients in this study makes it a preliminary report. More studies with more patients are needed before a final summary can be made. In the meantime, it might be best to go with whatever method your doctor has the most experience with.