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.

所有跟帖： 

• Other car's company -casinoeye- ♂ (0 bytes) () 05/12/2008 postreply 21:08:56

• 打电话给对方保险，索赔。一口咬定100%对方错，别松口。 -dogy- ♀ (0 bytes) () 05/12/2008 postreply 21:16:42

• Thank you very much. -jjj0704- ♀ (0 bytes) () 05/13/2008 postreply 06:45:40

• If you have full coverage, of course your own company. -cth163- ♂ (0 bytes) () 05/13/2008 postreply 07:38:09

• I have full coverage, can you pls explain why? -jjj0704- ♀ (0 bytes) () 05/13/2008 postreply 18:38:04

• 因为对方公司是能扣一点钱就是一点 -ma012- ♂ (156 bytes) () 05/14/2008 postreply 08:23:29