Insurance - how to determine write off vs repair?

[T3rminator]

Say your car is insured for $10,000, and you have a prang and need to make a claim, how does the insurance company determine whether to repair or to write off?

Obviously if the repair bill is above the cost of the insured amount, they will write it off.

But what if the repair bill is close to the insured amount? For example, lets say the damage will cost $9,500 to repair. Will they go ahead with repair or will they likely write it off?