I don't think anyone can predict for sure which surgery will work best for you. Both of these doctors are very experienced at PNE surgery so that isn't really much of a consideration. The approaches are different so it might be a matter of deciding which surgical approach would be best for you. I went to Bautrant because I had pelvic instability and I didn't want my sacrotuberous ligament cut. But some people have had their nerve entwined in the ST ligament so for them the TG approach would be better because Bautrant's approach doesn't address the ST ligament. At least when I watched him perform the TIR surgical approach, he did not access the ST ligament, so unless he's changed the procedure I would not expect to have the nerve released from the ST ligament. You can compare the 2 approaches here: http://www.pudendalhope.info/node/23
Bautrant originally used the TG approach but was not happy with the results so he developed the TIR approach. However, Dr. Conway originally used the TIR approach but later switched to the TG approach. The TG is most widely used and is considered to have the best visualization for the surgeon.
PNE since 2002. Started from weightlifting. PNE surgery from Dr. Bautrant, Oct 2004. Pain now is usually a 0 and I can sit for hours on certain chairs. No longer take medication for PNE. Can work full time and do "The Firm" exercise program. 99% cured from PGAD. PNE surgery was right for me but it might not be for you. Do your research.