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The price will not. It is a more advanced surgery, that is all there is to it. A larger incision, more sewing, more delicate procedure, more tying, more time under anesthesia. It takes maybe 5 minutes to neuter a male dog. Vasectomies take at least 4X that time with vets who are familiar with the procedure. You have to be a lot more cautious with organs you intend to keep in working condition.
If you're looking for something that will sterilize an animal in a safe matter and be as less intrusive as possible, I'd suggest reading into chemical castration. Neutering via zinc is being done today on a small population. I don't think it's at the point where it can be widely used yet, as sterilization is only something like 80% effective and takes many months for it to work. But I think chemical castration, when perfected, will be the answer to just about all animal overpopulation, including pets smaller than cats and rabbits, like hamsters and guinea pigs.
Don't get me wrong, I'm not against vasectomy and tubal ligation as a whole. If people want to do that, all power to them. However, I don't believe it will be the answer to pet overpopulation, and therefore don't believe it should replace spaying and neutering. The main factors of pet overpopulation include money ('it's too expensive to fix my pet' from pet owners) and time ('we don't have enough time to fix all of these animals today' from vets and vet techs). Both of those factors would be worsened by vasectomy's and tubal ligation's longer, more tedious procedure.
If people wanted to keep their animal's hormones, I would much rather them have their animal sterile, anyways. It's not a good thing to advocate to everyone, though. Keep in mind, the average dog owner can not take care of a high energy dog, let alone a dog with hormones still intact.