My car was hit by another car

it was their fault. I am in NJ, it is a no-fault state.
My insurance policy only cover 80% of medical expense.
Should I claim the other 20% to that person or let my
medical insurnace pick it up? My medical insurance policy
is a little bit tricky, if I ask them to pick up the bill,
it is equvalent to I pay the bill myself at the end.
This is my first accident, any suggestions? Thanks in advance.