I just spoke with a friend who is an insurance agent and here is her response. Keep in mind this is generally true in the state of Iowa and may be different where you live. The at-fault parties insurance company will more than likely replace the parts with "of like kind and quality". This will mean they will more than likely be aftermarket and not OEM Toyota parts. .
True...if you use the other company, they are going to try and "cheap out." If you file the claim with them, they will low ball, deny and stall as much as they can. They don't want to pay out anymore than they have to.
File a claim with your company, get your car fixed or totaled and let your insurance company go after their company.
As far compensation for diminished value that you may incur when trying to sell or trade a vehicle that has been in an accident, there is no payment for this.
Not attacking, but your friend is wrong. Any insurance company isn't going to come out and say, "Hey here's a check for diminished value." What I've learned in dealing with DV is you will have to file that claim with the other company insurance policy. Going alone they will tell you it doesn't exist. Get an attorney and have him fight it for you.
To help with a DV claim, upon receipt of a repaired car, document any/every flaw with pics and in writing. This will further strengthen your case about your car not being repaired to pre accident condition...therefore resulting in less value.
EDIT: DV probably isn't going to get paid out to you if you're driving a car with a year 19XX and older. 201X and above, yeah, you can get something.