Should I sign this letter or force them to fire me? What are the differences between my prospects with the two options?
If you can afford to do so, consult a lawyer. That way you will know all of your options, not just the most apparent ones. If you have no option other than to leave, then your decision should rest on whether you want to fight/contest your removal or not. If you don't contest it, then it is probably (subject to legal advice) better to sign the letter. But if you sign it, you are probably giving up options. 

But advice like this should come from a lawyer.