My insurance's company decision is different from the other person's insurance company's decision, what will happen next?

Note: my insurance company believes I am 0% at fault, while the other person's insurance company believes I am 100% at fault.

Should I sell my total loss car now(since my insurance will expire soon)? Or should I keep the car till final settlement(then I need to buy insurance for my car although I don't drive this car at all, it really wastes of my money).

Thanks.

Edit this page