Don't run off and have the car repaired immediately. If you do, you are relying solely on your carrier to subrogate to recover anything. If the other company writes a higher estimate, the half they offer you initially may be more than 50% of what this other shop already agreed to. Insurance companies write to repair cars to different standards. Sorry, but that's a fact. If you are insured by Lizard insurance, one of our customers hits you, and we take 50% responsibility, there's a good chance my 50% will pay for 100% of the level of quality repair you'll get from your own company. The are several companies out there where I simply cannot compete with their estimates.
There are also differences in the estimating software that will create different amounts. Meaning, instead of my comment about 5 adjusters writing 5 different estimates, if I used two different brands of software, you'd get two different estimates from the same person seeing the same damage and writing the "same" repairs.
At the very least, allow the other carrier to inspect the car prior to repairs and get their estimate.
There are also differences in the estimating software that will create different amounts. Meaning, instead of my comment about 5 adjusters writing 5 different estimates, if I used two different brands of software, you'd get two different estimates from the same person seeing the same damage and writing the "same" repairs.
At the very least, allow the other carrier to inspect the car prior to repairs and get their estimate.