To clarify the other responses:
If a section of the fence was damaged (8' for example), it's a repair, and you are entitled to the cost of repair.
If enough of the fence was damaged to require replacement of the entire length of fence then you are entitled to the replacement cost LESS depreciation.
I do agree that, in court, you are likely to be awarded more than 50% on a 6 year old fence. Cedar has a very long useful life.
But if you don't want to hassle with the driver's insurance company and/or court, make the claim on your homeowners policy, then let your insurance company deal with the other insurance company. You'll have a deductible but your insurance company will refund it to you when it collects.