I think the difference is that certain states require a rabies vaccine every year and others don't. Personally, I do the three year injection because there are usually some mild side effects, so why put them through that more often than necessary.
You should probably ask your Vet if they think the three year is more potent and might cause a more serious reaction. They would know best.
Maybe you would find this PetMd article valuable (see link below), regarding the 1 yr vs 3 yr issue. But, as noted above, it is still a state level determinant - that will likely change over time if you consider the information in this article. It would seem if you can get the 3-year, it would be the most logical route - it doesn't seem to be a potency issue from what I can tell. Rabies vaccines every year? Seriously? | PetMD
One of mine got the three-year version this year. He seemed to have reaction symptoms pretty bad for two or three days. Never was that bad before when he got the one-year version.