Not sure who to sue for damages

I live in Florida, and had an accident here. The other party was at fault and their insurance company will only pay half of the damages. I would like to know whether to sue the other party or their insurance company for all of the damages. I have received a check for half of the damages from the other party's insurance company, but have not cashed it. I would appreciate any advice or information you could provide. Thank you.

[I AM ALWAYS LIABLE]

My response:

This is what happens in a "No-Fault" insurance State. Next time it comes up for a Vote, vote "NO" on No-Fault.

In the meantime, talk to your own insurance company and see what they can (or more probably, won't) do for you.

Good luck amigo.

IAAL