The insurance company pays what the car is worth on the market, based on, for example, the Kelley Blue Book™ value. You can haggle over the classification the insurance company uses ("My car was a four-door, not a two-door, and it had air conditioning"), and that might increase the value. A qualification within the same category ("My car was in perfect condition" ) probably won't get you much more money.
If personal injury claims are involved, such as medical expenses or pain and suffering, negotiations get more complicated. An experienced car accident attorneycan negotiate all aspects of your claim and help win you a larger overall settlement.