Auto Insurance Claims: Appraisals from 2 auto insurance claims, auto insurance claims, initial estimates

Question
I was in an accident where the other driver did acknowledge they were at fault.  I had my insurance company appraise the car, then the other driver's insurance company asked to appraise since they accepted liability for the accident.  The other driver's insurance's appraisal is almost twice as much as mine.  My question is which insurance company should I submit the claim to as I thought that mine insurance company would work in my best interest?

Answer
I would submit the claim to the other party's insurance company, since there will be no deductible due at the completion of the work. I cannot explain why your company's estimate was half the liability carrier's, but insurance companies typically lowball their initial estimates in hopes that policyholders will pocket the check and not have their cars repaired. However, regardless of which company you submit the claim to, their offers are all subject to acceptance by a competent repair shop.