If Someone hit your car do you claim it on your insurance or theirs?

If they admit fault and their insurance company says they will pay for everything then it's been my experience that you get a choice. If you work through your own insurance company they may withhold your deductible amount until the other insurance company pays up. I believe that it makes sense to just work with the other guy's insurance company. They'll make an offer (if it was totaled) or ask you if you have a body shop preference and to take it there and they pay the bill. The deductible amount is not a factor since the other party is At Fault. In fact, I'm not sure why this isn't just standardized and made the common way to handle it, with the exception of if you believe that you're not being treated fairly.