Quiting is more satisfactory, but you get severance for being fired.
I've been in this situation twice.
The first time, I took the "I quit" route and had the manager backpedal so fast, I thought he was going to fall over.
The other, lets just say I got along much better with my Director, and after a skip 1-on-1 with the her, I had a new manager and my old one was doing "special projects."
Also, you have to be ready and willing to make it stick. If they call you on it, you have to walk. Else, no matter what happens with the current situation or future situation, they know you will back down.