The repairs the other side is liable for are the fair cost of repairs less any prior damage or depreciation. If the car is totaled out, the value they are liable for is the fair market value of the car, including deductions for damage, depreciation, mileage, and adding any salvage value.
If you did not have your own insurance, you are stuck with their evaluation. If you were insured, you're likely better off filing a claim with your own carrier.
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Mr. Hoffman gave you sound advice. The insurers have varying ways to measure the damage, but whether they look at the cost to restore the care to its "beat up" condition or look at the cost to restore it to as-new and then deduct t the cost to repair the prior damage, the numbers should be about the same.
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