If I was rear ended, will I get a better payout if I file the claim with my company instead of the company of the other driver?

If I file the claim with the other driver's company and my car is totaled, can I file with my company to get a better payout?

You won't be able to file multiple claims for the same accident. Your insurance company and the company of the other driver will settle on a final value for your car if it is considered a total loss so the payout would essentially be the same regardless of who pays the claim.