I used to have quite a bad overbite, so much that my bottom teeth used to dig into the roof of my mouth. I wasn't offered sugery, but i had orthodontic treatment for about 8 years! I started off with a plastic retainer in the top, to protect the roof of my mouth. Then i had retainers on the top and bottom with square blocks, that lock your jaw into a less overbitten position. These were the ugliest, most uncomfortable retainers i have ever worn, and were disgusting. You had to take them out before eating, and only being about 11 i would wrap them in a napkin in restaurants and forget....the amount of times the staff have had to go through the bins looking for them!!
After that, i had train tracks for 5 years. Now I have nice teeth, and my overbite isnt that bad at all, however I do have a really clicky jaw, which feels like it can almost click out of place if i eat something too chewy.
I think based on the length of my treatment, i would have rather had my jaw broken, however not personally experiencing the operation i will never know. Either way, i'm there now.
Good luck with your decision.