Also, a lot depends on your State law. If you are a no-fault state, it changes things. You will get nothing for pain and suffering until the medical bills are huge. It will occur in stages: first, up to the amount on YOUR policy for actual medical expense; then, the other company's policy, and then you can sue personally.
I know because I got hit in the rear at a red light last Spring. Naturally, I did the inquiries. No, I had no intention of being a profiteer or wise guy. But, my car was only 8 months old. We all know I'd take a big hit on the depreciation. The classic means to avoid being (financially) upside-down was to sue, or at least have the credible threat of suing, for injuries to get enough just to cover the car. But, we're no-fault so that could go nowhere and I was out $10,000. or a bit more.