Urgent! Cash settled?

Hit by a police car-- follow up.
The police report came out and concluded that the police officer is responsible for the accident, so my insurance company(AAA) granted to have my car repaired without my paying a cent. I took my car to the designated body shop and got an estimate at $3500. I asked the AAA agent who told me i can take cash settled which means that i can get a check(cash back) without having my car repaired. AAA will send an appraisel person to estimate the damage of my car and get an estimate which is below the amont of $3500 but i don't know how much lower. The amont of the check will be according the estimate of the appraisel person.
Since my car is not a good one and i want to sell it later, my question is:
SHould i take the check and have my car roughly repaired so that i can earn the difference or should i take my car repaired by the bodyshop?
Thanks a million