How to file a claim after no-fault accident?

I'm new here, could someone here please help. I had a minor accident last Sunday in Bronx, NY. Another car is tailgating and hit my car from behind on the highway. My new car has some scratch and the mufler has some damage but not serious. The other car has more damage. We called the police and they filed an accident report. When I called my insurance company (AllState) today, they told me I can either file a claim with my insurance company, or file a claim through the other driver's insurance company. Which way is better, can you advise please?

Many thanks.