Fired or quit:
No employer today is going to give a reference or tell anyone why you are no longer there, if they do and you can prove it, then you have a lawyer case.
Now taking that knowledge, and the fact that there is no lifetime employment "record". I really wouldnt care, unless 1 of 2 circumstances exist.
#1) If you plan on drawing unemployment, you can not do this if you quit, your employer knows this and he pays for your unemployment, he does not want you to draw and this is the #1 reason most employers, will "give you the opportunity" to resign. I have never filed for or drawn unemployment, cant comment on it, but I have paid it on a few employees. If I suspect someone is going that route today, Ill offer a 1 week severance in exchange for a signed resignation.
#2) Is there a severance package at hand? If they are offering money to walk then take it. You are never going to force an employer to give you an old job back (and if you could would you want it?) So if they are willing to pay you to leave dont blink an eye.
Im am a firm believer that things happen for a reason, if you are in the right here chances are better than average that you will look back in a year and say this is a blessing in disguise. My advice stems for my experience 2.5 years ago when I lost a good job, had an outstanding track record and was given no reason. I went off like a hot headed kid, called up m attorney brought in dozens of files of documentation and swore Id sue the pants off the owner. 30 months later I make more money, work less hours, actually enjoy my job and never look back. Use it as a springboard and go start fresh....