Do I need an implant for my missing canine? Also underbite and open bite braces and jaw surgery in the process. (photo)

Office one said they would take a few months to open up space for an implant($$$), have the implant done, then few months of braces, surgery, then braces again for a total of 2 years to finish up. Office two said an implant is not necessary, and what they would be doing is aligning the teeth so that top 1st premolar meets bottom canine, 2nd premolar hits bottom 1st premolar and so on. It would take less time to align, surgery, then more braces to align, total of ~15 months. Other costs equal.